ملخص كتاب الفيزياء السادس العلمي 2016

1. ‫ﻓﺼﻮل‬ ‫ﻣﻠﺨﺼﺎت‬
‫اﻟﻔﻴﺰﻳﺎء‬
‫ﻟﻠﺼﻒ‬‫اﻟﺴﺎدس‬‫اﻟﻌﻠﻤﻲ‬
)‫وﻣﻼﺣﻈﺎت‬ ‫ﻗﻮاﻧﻴﻦ‬(
‫إﻋﺪاد‬
‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬ ‫اﻟﻔﻴﺰﻳﺎء‬ ‫ﻣﺪرس‬
email/abuhussen_72@yahoo.com
www.facebook.com/saeedmuhi
2015 – 2016

2. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-3-
‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬:‫ﺎز‬‫ﺟﮭ‬ ‫ﻦ‬ ‫ﻋ‬ ‫ﺎرة‬‫ﻋﺒ‬ ‫ﻲ‬ ‫ھ‬‫ﺄﻟﻒ‬ ‫ﯾﺘ‬‫زوج‬ ‫ﻦ‬ ‫ﻣ‬)‫او‬‫ﺮ‬‫أﻛﺜ‬(‫ﺮ‬ ‫ﻏﯿ‬ ‫ﺪاءا‬ ‫اﺑﺘ‬ ‫ﺎزل‬‫ﻋ‬ ‫ﺎ‬ ‫ﺑﯿﻨﮭﻤ‬ ‫ﺼﻞ‬ ‫ﯾﻔ‬ ‫ﻠﺔ‬ ‫اﻟﻤﻮﺻ‬ ‫ﺼﻔﺎﺋﺢ‬ ‫اﻟ‬ ‫ﻦ‬ ‫ﻣ‬
‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫واﻟﻄﺎﻗﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺸﺤﻨﺎت‬ ‫ﻟﺘﺨﺰﯾﻦ‬ ‫ﺗﺴﺘﻌﻤﻞ‬ ‫ﻣﺸﺤﻮﻧﺘﯿﻦ‬.
‫ﺑﺎﻟﺮﻣﺰ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪواﺋﺮ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫وﯾﺮﻣﺰ‬‫او‬‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﺟﻤﯿﻊ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺮﻣﺰ‬ ‫ھﺬا‬ ‫وﯾﻨﻄﺒﻖ‬.
‫اﻟﻤﺘﻮازﻳﺘﻴﻦ‬ ‫اﻟﺼﻔﻴﺤﺘﻴﻦ‬ ‫ذات‬ ‫اﻟﻤﺘﺴﻌﺔ‬:
‫ﻀﮭﻤﺎ‬ ‫ﺑﻌ‬ ‫ﻦ‬ ‫ﻋ‬ ‫ﺰوﻟﺘﯿﻦ‬ ‫ﻣﻌ‬ ‫ﺎﺛﻠﺘﯿﻦ‬ ‫ﻣﺘﻤ‬ ‫ﺴﺘﻮﯾﺘﯿﻦ‬ ‫ﻣ‬ ‫ﻠﺘﯿﻦ‬ ‫ﻣﻮﺻ‬ ‫ﻔﯿﺤﺘﯿﻦ‬ ‫ﺻ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﻮازﯾﺘﯿﻦ‬ ‫اﻟﻤﺘ‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬ ‫اﻟ‬ ‫ذات‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﺎﻟﻒ‬ ‫ﺗﺘ‬
‫ﺎ‬‫ﻣﻨﮭﻤ‬ ‫ﻞ‬‫ﻛ‬ ‫وﻣﺴﺎﺣﺔ‬ ‫وﻣﺘﻮازﯾﺘﯿﻦ‬)A(‫ﺪ‬‫ﺑﺎﻟﺒﻌ‬ ‫ﻀﮭﻤﺎ‬‫ﺑﻌ‬ ‫ﻦ‬‫ﻋ‬ ‫ﺪان‬‫وﺗﺒﻌ‬)d(‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ﻮن‬‫ﺗﻜ‬‫ﺸﺤﻮﻧﺘﯿﻦ‬‫ﻣ‬ ‫ﺮ‬‫ﻏﯿ‬ ‫ﺪاءا‬‫اﺑﺘ‬‫ﺪ‬‫وﺑﻌ‬
‫ﻧﻮﻋﺎ‬ ‫وﻣﺨﺘﻠﻔﺘﯿﻦ‬ ‫ﻣﻘﺪارا‬ ‫ﻣﺘﺴﺎوﯾﺘﯿﻦ‬ ‫ﺷﺤﻨﺘﯿﻦ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﻋﻠﻰ‬ ‫ﺗﻈﮭﺮ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺷﺤﻦ‬.
♦‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺷﺤﻦ‬ ‫ﯾﺘﻢ‬ ‫ان‬ ‫ﺑﻌﺪ‬‫ﻮازﯾﺘﯿﻦ‬‫اﻟﻤﺘ‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ذات‬‫ﻰ‬‫اﻻﻋﻠ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ذات‬ ‫ﺼﻔﯿﺤﺔ‬‫اﻟ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫ﻛﮭﺮﺑ‬ ‫ﺪ‬‫ﺟﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺪ‬‫ﯾﺘﻮﻟ‬
)‫اﻟﻤﻮﺟﺐ‬ ‫اﻟﺠﮭﺪ‬(‫اﻻوطﺎ‬ ‫اﻟﺠﮭﺪ‬ ‫ذات‬ ‫واﻟﺼﻔﯿﺤﺔ‬)‫اﻟﺴﺎﻟﺐ‬ ‫اﻟﺠﮭﺪ‬(‫و‬‫ﺑﺎﻟﺮﻣﺰ‬ ‫ﻟﮫ‬ ‫ﯾﺮﻣﺰ‬)V∆(.
♦‫و‬‫و‬ ‫ﻗﺪ‬‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﺪار‬‫ﻣﻘ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺐ‬‫ﯾﺘﻨﺎﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﻓﺮق‬ ‫ان‬ ‫ﻋﻤﻠﯿﺎ‬ ‫ﺟﺪ‬)Q(‫ﻦ‬‫ﻣ‬ ‫أي‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬
‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬.
‫ان‬ ‫أي‬:
ttancons
V
Q
Q.
ttancons
1
VQV =
∆
⇒=∆⇒α∆
‫اﻟﺜﺎﺑﺖ‬ ‫واﻟﻤﻘﺪار‬)constant(‫ﺎﻟﺮﻣﺰ‬‫ﺑ‬ ‫ﺎ‬‫ﻟﮭ‬ ‫ﺰ‬‫وﯾﺮﻣ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﯾﺴﻤﻰ‬)C(.‫اﻟﻌ‬ ‫ﻮن‬‫ﯾﻜ‬ ‫ﺪﻣﺎ‬‫وﻋﻨ‬ ‫ﺬﻟﻚ‬‫ﻟ‬‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎزل‬
‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻓﺎن‬ ‫اﻟﮭﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫اﻟﻤﺘﺴﻌﺔ‬)C(‫ﻔﯿﺤﺘﯿﮭﺎ‬‫ﺻ‬ ‫ﻣﻦ‬ ‫أي‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫واﻟﺸﺤﻨﺔ‬)Q(‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫وﻓ‬
‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬)V∆(‫اﻟﺘﺎﻟﻲ‬ ‫ﺑﺎﻟﺸﻜﻞ‬ ‫ﺗﻜﺘﺐ‬:
♦‫و‬ ‫ﺎراد‬‫ﺑﺎﻟﻔ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﺎس‬‫ﺗﻘ‬‫ﺰه‬‫رﻣ‬)F(‫ﺰه‬‫ورﻣ‬ ‫ﺎﻟﻜﻮﻟﻮم‬‫ﺑ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﺎس‬‫وﺗﻘ‬ ‫ﺰاءه‬‫اﺟ‬ ‫او‬)C(‫ﺰاءه‬‫اﺟ‬ ‫او‬‫ﺮق‬‫ﻓ‬ ‫ﺎس‬‫وﯾﻘ‬
‫ورﻣﺰه‬ ‫ﺑﺎﻟﻔﻮﻟﻂ‬ ‫اﻟﺠﮭﺪ‬)V(‫ﻟﺬﻟﻚ‬)F=C/V. (
♦‫ﻮم‬ ‫اﻟﻜﻮﻟ‬ ‫ﺰاء‬ ‫اﺟ‬ ‫او‬ ‫ﺎراد‬ ‫اﻟﻔ‬ ‫ﺰاء‬ ‫اﺟ‬‫ﻲ‬ ‫اﻟﻤﻠ‬ ‫ﻲ‬ ‫ھ‬)m(‫ﺎﯾﻜﺮو‬ ‫واﻟﻤ‬)µ(‫ﺎﻧﻮ‬ ‫واﻟﻨ‬)n(‫ﻮ‬ ‫واﻟﺒﯿﻜ‬)P(‫ﺰاء‬ ‫اﻻﺟ‬ ‫ﺬه‬ ‫ھ‬ ‫ﺴﻤﻰ‬ ‫وﺗ‬
‫اﻟﻘﯿﺎس‬ ‫ﺑﺎدﺋﺎت‬‫ﺣﯿﺚ‬:
m=10-3
, µ=10-6
, n=10-9
, p=10-12
♦‫اﻟﺘﻌﺮﯾﻒ‬ ‫ﺑﻤﻮﺟﺐ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻗﺎﻧﻮن‬ ‫اﺳﺘﺨﺪام‬ ‫ﺣﺎل‬ ‫ﻓﻲ‬)
V
Q
C
∆
=(‫ﺪة‬‫اﻟﻮﺣ‬ ‫ﻰ‬‫اﻟ‬ ‫اﻟﺒﺎدﺋﺔ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺤﻮﯾﻞ‬ ‫اﻟﻀﺮوري‬ ‫ﻣﻦ‬ ‫ﻟﯿﺲ‬
‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺎدﺋﺔ‬ ‫ھﻲ‬ ‫اﻟﺴﻌﺔ‬ ‫وﺑﺎدﺋﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﺑﺎدﺋﺔ‬ ‫ھﻲ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺎدﺋﺔ‬ ‫ﺗﻜﻮن‬ ‫ان‬ ‫ﺑﺸﺮط‬.
‫س‬/‫اﻻﺳﺎﺳﯿﺔ‬ ‫ﺑﺎﻟﻮﺣﺪات‬ ‫اﻟﻔﺎراد‬ ‫اﺷﺘﻖ‬.
‫ج‬/
2
22
2
222
m.kg
s.C
m.
s
m
.kg
C
m.N
C
J
C
C
J
C
V
C
F ======
‫ﺍﳌﺘﺴﻌﺔ‬ ‫ﺻﻔﻴﺤﺘﻲ‬ ‫ﺑﲔ‬ ‫ﺍﻟﻜﻬﺮﺑﺎﺋﻲ‬ ‫ﺎﻝ‬‫ﺍ‬:‫ﻧﺴﺒﺔ‬ ‫ھﻮ‬‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬)V∆(‫ﺪ‬‫اﻟﺒﻌ‬ ‫ﻰ‬‫إﻟ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬)d(‫ﯿﻦ‬‫ﺑ‬
‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬.
‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻓﺎن‬ ‫ھﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﺎزل‬ ‫ﯾﻜﻮن‬ ‫وﻋﻨﺪﻣﺎ‬ ‫اﻟﺘﻌﺮﯾﻒ‬ ‫ھﺬا‬ ‫وﺑﻤﻮﺟﺐ‬ ‫ﻟﺬﻟﻚ‬)E(
‫اﻟﺠﮭﺪ‬ ‫وﻓﺮق‬)V∆(‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫واﻟﺒﻌﺪ‬)d(‫ھﻲ‬:
)‫ﻫﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫اﻟﺼﻔﻴﺤﺘﻴﻦ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻌﺎزل‬ ‫ﻛﺎن‬ ‫اذا‬(
d
V
E
∆
=
V
Q
C
∆
=
‫ﻧﯿﻮﺗﻦ‬ ‫ھﻲ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫وﺣﺪة‬‫ﻛﻮﻟﻮم‬)N/C(‫ﻓﻮﻟﻂ‬ ‫او‬‫ﻣﺘﺮ‬)v/m(

3. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-4-
‫ﻓﺎن‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ھﺬه‬ ‫إﻟﻰ‬ ‫اﺳﺘﻨﺎدا‬:
1(‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫اﻟﻤﺠ‬)E(‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺐ‬‫ﯾﺘﻨﺎﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬)∆V(‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺒﻌ‬ ‫ﻮت‬‫ﺑﺜﺒ‬
‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬ ‫اﻟﺒﻌﺪ‬ ‫ﻣﻊ‬ ‫ﻋﻜﺴﯿﺎ‬ ‫وﺗﻨﺎﺳﺒﺎ‬‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﺠﮭﺪ‬.
‫ﻟﺬﻟﻚ‬:
E α ∆V ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫ﺑﺜﺒﻮت‬
E α
d
1
‫ﺑﺎﻟﺒﻄﺎرﯾﺔ‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺜﺒﺖ‬ ‫ﺣﯿﺚ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬
2(‫ﻛ‬ ‫ﻛﺎن‬ ‫إذا‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﯾﺜﺒﺖ‬‫واﺣﺪ‬ ‫ان‬ ‫ﻓﻲ‬ ‫ﻣﺘﻐﯿﺮﯾﻦ‬ ‫او‬ ‫ﺛﺎﺑﺘﯿﻦ‬ ‫واﻟﺒﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻣﻦ‬ ‫ﻞ‬.
‫ﻟﻠﻤﺘﺴﻌﺔ‬ ‫ﺍﻟﻜﻬﺮﺑﺎﺋﻲ‬ ‫ﺎﻝ‬‫ﺍ‬ ‫ﰲ‬ ‫ﺍﳌﺨﺘﺰﻧﺔ‬ ‫ﺍﻟﻄﺎﻗﺔ‬ ‫ﺣﺴﺎﺏ‬:
♦‫ﺔ‬‫اﻟﻄﺮدﯾ‬ ‫ﺔ‬‫اﻟﻌﻼﻗ‬ ‫ﺢ‬‫ﯾﻮﺿ‬ ‫ﺎﻧﻲ‬‫ﺑﯿ‬ ‫ﻂ‬‫ﻣﺨﻄ‬ ‫ﻢ‬‫رﺳ‬ ‫ﻼل‬‫ﺧ‬ ‫ﻣﻦ‬ ‫ﻟﻠﻤﺘﺴﻌﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺣﺴﺎب‬ ‫ﯾﻤﻜﻦ‬
‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﯿﻦ‬)Q(‫وﻓﺮق‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﻣﻦ‬ ‫أي‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫اﻟﺠﮭﺪ‬)∆V(‫ﺎ‬‫ﺑﯿﻨﮭﻤ‬.‫ﺴﺎب‬‫ﺣ‬ ‫ﻼل‬‫ﺧ‬ ‫ﻦ‬‫وﻣ‬
‫اﻟﻤﺜﻠﺚ‬ ‫ﻣﺴﺎﺣﺔ‬)‫اﻟﻤﺜﻠﺚ‬ ‫ﻣﺴﺎﺣﺔ‬=
2
1
‫اﻟﻘﺎﻋﺪة‬×‫اﻻرﺗﻔﺎع‬(
‫ﺪة‬ ‫اﻟﻘﺎﻋ‬ ‫ﺚ‬‫ﺣﯿ‬)‫ﻞ‬‫ﺗﻤﺜ‬∆V(‫ﺎع‬ ‫اﻻرﺗﻔ‬ ،)‫ﺸﺤﻨﺔ‬ ‫اﻟ‬ ‫ﺪار‬ ‫ﻣﻘ‬ ‫ﻞ‬‫ﯾﻤﺜ‬Q(‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬ ‫اﻟﻤﺠ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺔ‬ ‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺔ‬ ‫اﻟﻄﺎﻗ‬ ‫ﺴﺎب‬ ‫ﺣ‬ ‫ﻦ‬ ‫ﯾﻤﻜ‬
‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫ﻟﻠﻤﺘﺴﻌﺔ‬:
‫ﺎﻟﺠﻮل‬‫ﺑ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺗﻘﺎس‬)J(‫ﺎﻟﻜﻮﻟﻮم‬‫ﺑ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻮن‬‫ﺗﻜ‬ ‫ﺪﻣﺎ‬‫ﻋﻨ‬)C(‫ﺎﻟﻔﻮﻟﻂ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫وﻓ‬)V(
‫ﺑﺎﻟﻔﺎرد‬ ‫واﻟﺴﻌﺔ‬)F. (
‫اﻟﺘﺎﻟﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﻘﺪرة‬ ‫ﺣﺴﺎب‬ ‫ﯾﻤﻜﻦ‬ ‫ﻛﺬﻟﻚ‬:
‫اﻟﻘﺪر‬ ‫ﻗﯿﺎس‬ ‫وﺣﺪة‬‫ﺑﺎﻟﺜﺎﻧﯿﺔ‬ ‫واﻟﺰﻣﻦ‬ ‫ﺑﺎﻟﺠﻮل‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻟﻮاط‬ ‫ھﻲ‬ ‫ة‬.
‫ﻣﻼﺣﻈﺎﺕ‬/
v‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬:
Q.V
2
1
PE ∆=
‫ﺮ‬‫ﻓ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺐ‬‫ﺗﺘﻨﺎﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ان‬ ‫ﺪ‬‫ﻧﺠ‬‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻮت‬‫ﺑﺜﺒ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ق‬
‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫وﺗﺘﻨﺎﺳﺐ‬‫ﻣ‬ ‫طﺮدﯾﺎ‬ ‫وﺗﺘﻨﺎﺳﺐ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬ ‫اﻟﺸﺤﻨﺔ‬‫اﻟﺴﻌﺔ‬ ‫ﺑﺜﺒﻮت‬ ‫واﻟﺸﺤﻨﺔ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻊ‬.
‫ان‬ ‫أي‬:
or
1
2
1
2
Q
Q
PE
PE
)constV(QPE =⇒=∆∝
C
Q
2
1
PEor)V(.C
2
1
PEorQ.V
2
1
PE
2
electric
2
electricelectric =∆=∆=
)t(time
PE
)P(Power electric
=
1
2
1
2
V
V
PE
PE
)constQ(VPE
∆
∆
=⇒=∆∝

4. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-5-
or
v‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬:
2
)V(.C
2
1
PE ∆=
‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫ﺗﺘﻨﺎﺳﺐ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ان‬ ‫ﻧﺠﺪ‬‫ﻊ‬‫ﻣﺮﺑ‬‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﻮت‬‫ﺑﺜﺒ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫وﺗﺘﻨﺎﺳﺐ‬‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫وﻣﺮﺑﻊ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫وﺗﺘﻨﺎﺳﺐ‬.
‫ان‬ ‫أي‬:
or
or
v‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬:
C
Q
2
1
PE
2
=
‫ﻧﺠﺪ‬‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﻮت‬‫ﺑﺜﺒ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻊ‬‫ﻣﺮﺑ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺐ‬‫ﺗﺘﻨﺎﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ان‬
‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻊ‬ ‫ﻋﻜﺴﯿﺎ‬ ‫وﺗﺘﻨﺎﺳﺐ‬‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻊ‬ ‫وﻋﻜﺴﯿﺎ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻣﺮﺑﻊ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫وﺗﺘﻨﺎﺳﺐ‬.
‫ان‬ ‫أي‬:
or
or
2
12
2
21
1
2
2
Q.C
Q.C
PE
PE
)constV(
C
Q
PE =⇒=∆∝
2
11
2
22
1
22
)V.(C
)V.(C
PE
PE
)constQ()V.(CPE
∆
∆
=⇒=∆∝
2
1
1
2
C
C
PE
PE
)constQ(
C
1
PE =⇒=∝
2
1
2
2
1
22
Q
Q
PE
PE
)constC(QPE =⇒=∝
1
2
1
2
C
C
PE
PE
)constV(CPE =⇒=∆∝
2
1
2
2
1
22
V
V
PE
PE
)constC(VPE
∆
∆
=⇒=∆∝
11
22
1
2
Q.V
Q.V
PE
PE
)constC(Q.VPE
∆
∆
=⇒=∆∝

5. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-6-
‫س‬/‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺗﺼﺒﺢ‬ ‫اﻟﺴﻌﺔ‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺘﻀﺎﻋﻒ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫رﯾﺎﺿﯿﺎ‬ ‫اﺛﺒﺖ‬
‫؟‬ ‫اﻣﺜﺎل‬ ‫ارﺑﻌﺔ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬
‫ج‬/
12
1111112
1212
222
PE4PE
)Q.V
2
1
(4)Q.V4(
2
1
)Q2).(V2(
2
1
PE
)ttanconsC(Q2QV2V
Q.V
2
1
PE
=∴
∆=∆=∆=∴
==⇒∆=∆
∆=
Q
‫س‬/‫ﺔ‬‫اﻟﺜﺎﻧﯿ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﻊ‬‫رﺑ‬ ‫اﻻوﻟﻰ‬ ‫ﺳﻌﺔ‬ ‫ﻣﺘﺴﻌﺘﺎن‬‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﻌﻒ‬‫ﺿ‬ ‫ﻔﯿﺤﺘﯿﮭﺎ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫وﻓ‬
‫اﻟﺜﺎﻧﯿﺔ‬‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﻣﻨﮭﻤﺎ‬ ‫ﻛﻞ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺑﺎن‬ ‫اﺛﺒﺖ‬.
‫ج‬/
21
2
1
2
2
2
2
2
1
2
22
2
22
2
1
2121
2
22
2
11
2
1
2
22
2
11
2
1
PEPE1
PE
PE
)V(
)V(4
4
1
PE
PE
)V.(C
)V2.(C
4
1
PE
PE
V2V,C
4
1
C
)V.(C
)V.(C
PE
PE
)V.(C
2
1
)V.(C
2
1
PE
PE
=⇒=⇒
∆
∆×
=⇒
∆
∆
=∴
∆=∆=
∆
∆
=⇒
∆
∆
=
Q
‫ﺍﻟﻜﻬﺮﺑﺎﺋﻲ‬ ‫ﺍﻟﻌﺎﺯﻝ‬:)Dielectric(
‫ﻧﻮﻋﻴﻦ‬ ‫إﻟﻰ‬ ‫ﻛﻬﺮﺑﺎﺋﻴﺎ‬ ‫اﻟﻌﺎزﻟﺔ‬ ‫اﻟﻤﻮاد‬ ‫ﺗﺼﻨﻒ‬:
1-‫اﻟﻘﻄ‬ ‫اﻟﻌﻮازل‬‫ﺒﻴﺔ‬.2-‫اﻟﻘﻄﺒﻴﺔ‬ ‫ﻏﻴﺮ‬ ‫اﻟﻌﻮازل‬.
♦‫ﺳﯿﻜﻮن‬ ‫ﻋﺎزل‬ ‫ﻋﻠﻰ‬ ‫ﺗﺤﺘﻮي‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺤﺼﻞ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﺎن‬ ‫اﻟﻌﺎزل‬ ‫ﻧﻮﻋﻲ‬ ‫ﻛﻼ‬ ‫ﻓﻲ‬:
‫ﺣﯿﺚ‬:
Ek:، ‫اﻟﻌﺎزل‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺤﺼﻞ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬E:‫اﻟ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺆﺛﺮ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬‫اﻟﻔﺮاغ‬ ‫ﺑﻮﺟﻮد‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬
Ed:‫اﻟﻌﺎزل‬ ‫داﺧﻞ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬
‫اﻟﻤﺠﺎ‬ ‫ان‬ ‫أي‬‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺼﻞ‬‫اﻟﻤﺤ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ل‬‫ﺴﻌﺔ‬‫ﻣﺘ‬‫ﺼﺪر‬‫اﻟﻤ‬ ‫ﻦ‬‫ﻋ‬ ‫ﺼﻠﺔ‬‫وﻣﻨﻔ‬ ‫ﺸﺤﻮﻧﺔ‬‫ﻣ‬)‫ﺔ‬‫اﻟﺒﻄﺎرﯾ‬(‫ﺴﺒﺔ‬‫ﺑﻨ‬ ‫ﻞ‬‫ﯾﻘ‬‫ﺖ‬‫ﺛﺎﺑ‬
‫اﻟﻌﺰل‬)k(‫ﻓﯿﻜﻮن‬:
dk EEE −= ‫ﯾﻜﻮ‬‫اﻷﺻﻠﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﺑﺎﺗﺠﺎه‬ ‫اﻟﻤﺤﺼﻞ‬ ‫اﻟﻤﺠﺎل‬ ‫اﺗﺠﺎه‬ ‫ن‬

6. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-7-
‫و‬‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺔ‬‫اﻟﻌﻼﻗ‬ ‫ان‬ ‫ﺎ‬‫ﺑﻤ‬)V∆(‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫واﻟﻤﺠ‬)E(‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺒﻌ‬ ‫ﻮت‬‫ﺑﺜﺒ‬ ‫ﺔ‬‫طﺮدﯾ‬)d(‫ﺎن‬‫ﻓ‬ ‫ﺬﻟﻚ‬‫ﻟ‬
‫ﺼﺪر‬ ‫اﻟﻤ‬ ‫ﻦ‬ ‫ﻋ‬ ‫ﺼﻠﺔ‬ ‫وﻣﻨﻔ‬ ‫ﺸﺤﻮﻧﺔ‬ ‫ﻣ‬ ‫ﺴﻌﺔ‬ ‫ﻣﺘ‬ ‫ﻔﯿﺤﺘﻲ‬ ‫ﺻ‬ ‫ﯿﻦ‬ ‫ﺑ‬ ‫ﺎزل‬ ‫اﻟﻌ‬ ‫ﺎل‬ ‫ادﺧ‬)‫ﺔ‬ ‫اﻟﺒﻄﺎرﯾ‬(‫ﺼﻔﯿﺤﺘﯿﻦ‬ ‫اﻟ‬ ‫ﯿﻦ‬ ‫ﺑ‬ ‫ﺪ‬ ‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﯿﻘﻠﻞ‬ ‫ﺳ‬
)kV∆(‫ﺑﻨﺴﺒﺔ‬‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬)k(‫وﻛ‬ ‫اﻟﮭﻮاء‬ ‫او‬ ‫ﺑﺎﻟﻔﺮاغ‬ ‫ﻗﯿﻤﺘﮫ‬ ‫ﻋﻦ‬‫ﯾﻠﻲ‬ ‫ﻤﺎ‬:
k
kk
k V
k
Ed
d
V
k
E
d
V
E
d
V
E ∆=⇒
∆
=⇒
∆
=⇒
∆
=
‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬:
‫وﺣﯿﺚ‬‫اﻟﺸﺤﻨﺔ‬ ‫ﻣﻘﺪار‬ ‫ﺛﺒﻮت‬ ‫ﻋﻨﺪ‬ ‫ﺻﻔﯿﺤﺘﯿﮭﺎ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺠﮭﺪ‬ ‫وﻓﺮق‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫ﺑﯿﻦ‬ ‫ﻋﻜﺴﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ان‬)‫ﺖ‬‫ﻛﺎﻧ‬ ‫اذا‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﺗﺜﺒﺖ‬
‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬(‫ﺎن‬‫ﻓ‬‫ﺎل‬‫إدﺧ‬‫ﯿﺆدي‬‫ﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎزل‬‫اﻟﻌ‬‫ﺎ‬‫زﯾ‬ ‫ﻰ‬‫إﻟ‬‫ﻌﺘﮭﺎ‬‫ﺳ‬ ‫دة‬‫ﺰل‬‫اﻟﻌ‬ ‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﺴﺒﺔ‬‫ﺑﻨ‬
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬)k(‫اﻟﻔﺮا‬ ‫ﺑﻮﺟﻮد‬ ‫ﺳﻌﺘﮭﺎ‬ ‫ﻋﻦ‬‫اﻟﮭﻮاء‬ ‫او‬ ‫غ‬.
V
Q
k
k
V
Q
V
Q
C
k
k
k
∆
=
∆
=
∆
=
‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬:
‫ﺣﯿﺚ‬:
CK:‫اﻟﻌﺎزل‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬
C:‫اﻟﮭﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬
k:‫اﻟﻌﺎزﻟﺔ‬ ‫ﻟﻠﻤﺎدة‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬‫وھﻮ‬‫ﻟﻠﻤﺎدة‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﻤﺎﺣﯿﺔ‬‫اﻟﻮﺣﺪات‬ ‫ﻣﻦ‬ ‫ﻣﺠﺮد‬ ‫ﻋﺪد‬ ‫وھﻮ‬.
‫اﻟﻜﮫﺮﺑﺎﺋﻲ‬ ‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬)k: (‫ﻧﺴﺒﺔ‬ ‫ھﻮ‬‫ﻮ‬‫وھ‬ ‫اﻟﮭﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫اﻟﻰ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬
‫اﻟﻌﺎزل‬ ‫ﻟﻠﻮﺳﻂ‬ ‫ﻣﻤﯿﺰة‬ ‫ﺻﻔﺔ‬.‫أن‬ ‫أي‬
‫ﻋﺎﺯﻝ‬ ‫ﺍﺩﺧﺎﻝ‬ ‫ﻋﻨﺪ‬‫ﻋﺰﻟﻪ‬ ‫ﺛﺎﺑﺖ‬)k(‫ﻓﺎﻥ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﺻﻔﻴﺤﺘﻲ‬ ‫ﺑﲔ‬:
1-‫ﺰداد‬‫ﺗ‬ ‫ﻌﺘﮭﺎ‬‫ﺳ‬‫ﺰل‬‫اﻟﻌ‬ ‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﺴﺒﺔ‬‫ﺑﻨ‬)k(‫ام‬ ‫ﺼﺪر‬ ‫ﺑﺎﻟﻤ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﺎ‬‫ﻛﻮﻧﮭ‬ ‫ﻦ‬ ‫ﻋ‬ ‫ﺮ‬‫اﻟﻨﻈ‬ ‫ﺾ‬ ‫وﺑﻐ‬ ‫ﻮاء‬‫اﻟﮭ‬ ‫او‬ ‫ﺎﻟﻔﺮاغ‬ ‫ﺑ‬ ‫ﻌﺘﮭﺎ‬‫ﺳ‬ ‫ﻦ‬ ‫ﻋ‬
‫اﻻﺗﯿﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬ ‫ﻋﻨﮫ‬ ‫ﻣﻨﻔﺼﻠﺔ‬:
‫ﻋﻨﻪ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫ام‬ ‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
2-‫ﺰداد‬‫ﺗ‬ ‫ان‬ ‫ﺎ‬ ‫اﻣ‬ ‫ﻔﯿﺤﺘﯿﮭﺎ‬ ‫ﺻ‬ ‫ﻦ‬ ‫ﻣ‬ ‫أي‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺔ‬ ‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬‫ﺴﺒﺔ‬ ‫ﺑﻨ‬)k()‫اذا‬‫ﺼﺪر‬ ‫ﺑﺎﻟﻤ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﺖ‬‫ﻛﺎﻧ‬(‫ﻻ‬ ‫او‬‫ﺎﺛﺮ‬ ‫ﺗﺘ‬
)‫ﺛﺎﺑﺘﺔ‬ ‫ﺗﺒﻘﻰ‬(‫اﻻﺗﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻓﻲ‬ ‫ﻛﻤﺎ‬ ‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬:
CkCK =
‫ﻣﻼﺣﻈﺎت‬
Ck = k C
k
V
Vk
∆
=∆
k
E
EK =
C
C
k K
=

7. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-8-
‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
or
‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
‫اﻟﻌﺎزل‬ ‫ﻗﺒﻞ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ان‬ ‫أي‬.
3-‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﻰ‬‫ﯾﺒﻘ‬ ‫ان‬ ‫ﺎ‬‫اﻣ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬)‫ﺼﺪر‬‫ﺑﺎﻟﻤ‬ ‫ﺼﻠﺔ‬‫ﻣﺘ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺖ‬‫ﻛﺎﻧ‬ ‫اذا‬(‫ﻞ‬‫ﯾﻘ‬ ‫او‬‫ﺴﺒﺔ‬‫ﺑﻨ‬
)k(‫اﻟﮭﻮاء‬ ‫او‬ ‫ﺑﺎﻟﻔﺮاغ‬ ‫ﻗﯿﻤﺘﮫ‬ ‫ﻋﻦ‬)‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬(‫اﻟﺘﺎﻟﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻓﻲ‬ ‫ﻛﻤﺎ‬:
‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
‫اﻟﻌﺎزل‬ ‫ﻗﺒﻞ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺴﺎوي‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ان‬ ‫أي‬.
or
‫اذا‬‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬
‫ﺖ‬‫ﻛﺎﻧ‬ ‫ﻮ‬ ‫ﻓﻠ‬ ‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﻰ‬ ‫ﯾﺒﻘ‬ ‫ﺮ‬‫واﻻﺧ‬ ‫ﺮ‬‫ﯾﺘﻐﯿ‬ ‫ﺪھﻤﺎ‬ ‫ﻓﺎﺣ‬ ‫ﺪ‬ ‫واﺣ‬ ‫ان‬ ‫ﻲ‬‫ﻓ‬ ‫ﺮان‬‫ﯾﺘﻐﯿ‬ ‫ﻻ‬ ‫ﺪ‬ ‫اﻟﺠﮭ‬ ‫ﺮق‬‫وﻓ‬ ‫ﺸﺤﻨﺔ‬ ‫اﻟ‬ ‫ﺎن‬ ‫ﻓ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﻮد‬ ‫ﺑﻮﺟ‬ ‫ﺬﻟﻚ‬‫ﻟ‬
‫ا‬‫ﻣﺘﺼﻠﺔ‬ ‫ﻟﻤﺘﺴﻌﺔ‬‫ﺑﺎﻟﺒﻄﺎرﯾﺔ‬‫ﺗﺘﻐﯿﺮ‬)‫ﺗﺰداد‬(‫ﺼﻠﺔ‬‫ﻣﻨﻔ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺖ‬‫ﻛﺎﻧ‬ ‫ﻮ‬‫وﻟ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫وﯾﺜﺒﺖ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺔ‬ ‫ﺑﻌﻼﻗﺔ‬ ‫اﻟﺸﺤﻨﺔ‬
‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﻋﻦ‬‫ﯾﺘﻐﯿ‬‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺮ‬)‫ﯾﻘﻞ‬(‫اﻟﺸﺤﻨﺔ‬ ‫وﺗﺜﺒﺖ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻊ‬ ‫ﻋﻜﺴﯿﺔ‬ ‫ﺑﻌﻼﻗﺔ‬.
4-‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﻰ‬‫ﯾﺒﻘ‬ ‫ان‬ ‫ﺎ‬‫اﻣ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬)‫ﺼﺪر‬‫ﺑﺎﻟﻤ‬ ‫ﺼﻠﺔ‬‫ﻣﺘ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺖ‬‫ﻛﺎﻧ‬ ‫اذا‬(‫ﺴﺒﺔ‬‫ﺑﻨ‬ ‫ﻞ‬‫ﯾﻘ‬ ‫او‬)k(
‫اﻟﮭﻮاء‬ ‫او‬ ‫ﺑﺎﻟﻔﺮاغ‬ ‫ﻗﯿﻤﺘﮫ‬ ‫ﻋﻦ‬)‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬(‫اﻟﺘﺎﻟﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻓﻲ‬ ‫ﻛﻤﺎ‬:
‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
‫اﻟﻌﺎزل‬ ‫ﻗﺒﻞ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﯾﺴﺎوي‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ان‬ ‫أي‬.
or
‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
5-‫اﻣ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬‫ﺰداد‬‫ﺗ‬ ‫ان‬ ‫ﺎ‬‫ﺴﺒﺔ‬‫ﺑﻨ‬(k)‫ﻮت‬‫وﺛﺒ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﺎدة‬‫زﯾ‬ ‫ﺴﺒﺐ‬‫ﺑ‬
‫ﺪ‬ ‫اﻟﺠﮭ‬ ‫ﺮق‬ ‫ﻓ‬)‫ﺼﺪر‬ ‫ﺑﺎﻟﻤ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﺖ‬ ‫ﻛﺎﻧ‬ ‫اذا‬(‫ﺴﺒﺔ‬ ‫ﺑﻨ‬ ‫ﻞ‬ ‫ﺗﻘ‬ ‫او‬)k(‫ﺸﺤﻨﺔ‬ ‫اﻟ‬ ‫ﻮت‬ ‫وﺛﺒ‬ ‫ﺪ‬ ‫اﻟﺠﮭ‬ ‫ﺮق‬ ‫ﻓ‬ ‫ﺼﺎن‬ ‫ﻧﻘ‬ ‫ﺴﺒﺐ‬ ‫ﺑ‬
)‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬(‫اﻻﺗﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻓﻲ‬ ‫وﻛﻤﺎ‬.
‫اﻟ‬ ‫ﻟﻠﻤﺘﺴﻌﺔ‬‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻤﺘﺼﻠﺔ‬
or
‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫اﻟﻤﻨﻔﺼﻠﺔ‬ ‫ﻟﻠﻤﺘﺴﻌﺔ‬
k
PE
PEk =
PEkPEk =
k
E
Ek =
EEK =
k
V
Vk
∆
=∆
VVK ∆=∆
QQK =
QkQK =

8. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-9-
‫اﻟﻤﺘﻮازﯾﺘﯿﻦ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ذات‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫ﻋﻠﯿﮭﺎ‬ ‫ﺗﻌﺘﻤﺪ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻌﻮاﻣﻞ‬:
1-‫اﻟﺴﻄﺤﯿﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬)A(‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ﻦ‬‫ﻣ‬ ‫ﻞ‬‫ﻟﻜ‬ ‫اﻟﻤﺘﻘﺎﺑﻠﺔ‬:‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﺐ‬‫ﺗﺘﻨﺎﺳ‬ ‫ﺚ‬‫ﺣﯿ‬)C(‫ﺴﺎﺣﺔ‬‫اﻟﻤ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺒﺎ‬‫ﺗﻨﺎﺳ‬
‫اﻟﺴﻄﺤ‬‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﻣﻦ‬ ‫ﻟﻜﻞ‬ ‫اﻟﻤﺘﻘﺎﺑﻠﺔ‬ ‫ﯿﺔ‬‫اﻟﺒﻌﺪ‬ ‫ﺑﺜﺒﻮت‬)d(‫و‬‫اﻟﻮﺳﻂ‬‫اﻟﻌﺎزل‬.‫ان‬ ‫أي‬:)AC( α
2-‫اﻟﺒﻌﺪ‬)d(‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬.‫ﻋﻜﺴﯿﺎ‬ ‫ﻣﻌﮫ‬ ‫وﺗﺘﻨﺎﺳﺐ‬‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﺑﺜﺒﻮت‬)A(‫اﻟﻌﺎزل‬ ‫واﻟﻮﺳﻂ‬.‫ان‬ ‫أي‬:)
d
1
C( α.
3-‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﺎزل‬ ‫اﻟﻮﺳﻂ‬ ‫ﻧﻮع‬:‫ﺗ‬ ‫ﺣﯿﺚ‬‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫ﺰداد‬‫ﺑﺈدﺧﺎل‬‫ﻋﺎزﻟﺔ‬ ‫ﻣﺎدة‬‫ﺎ‬‫ﻛﮭﺮﺑﺎﺋﯿ‬‫ﻦ‬‫ﻣ‬ ‫ﺪﻻ‬‫ﺑ‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ﯿﻦ‬‫ﺑ‬
‫اﻟﮭﻮاء‬‫أو‬‫اﻟﻔﺮاغ‬‫اﻟﺴﻄﺤﯿﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﺑﺜﺒﻮت‬)A(‫واﻟﺒﻌﺪ‬)d.(‫ﺣﯿﺚ‬:Ck = K C
‫اﻟﻌ‬ ‫ﯾﻜﻮن‬ ‫وﻋﻨﺪﻣﺎ‬‫ﺎ‬‫اﻟﺒﻌﺪ‬ ‫ﻣﻊ‬ ‫وﻋﻜﺴﯿﺎ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫ﺗﺘﻨﺎﺳﺐ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻓﺎن‬ ‫ھﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫زل‬)
d
A
Cα(‫ﻟﺬﻟﻚ‬‫ﻓﺎ‬‫ن‬:
‫ﺣﯿﺚ‬:
ο
ε:‫وﯾﺴﻤﻰ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫ﻋﺎزﻻ‬ ‫اﻟﮭﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫ﻛﺎن‬ ‫اذا‬ ‫اﻟﺘﻨﺎﺳﺐ‬ ‫ﺛﺎﺑﺖ‬‫اﻟﻔﺮاغ‬ ‫ﺳﻤﺎﺣﯿﺔ‬‫وﻣﻘﺪارھﺎ‬
)8.85×10 – 12
C2
/ N . m2
=ºЄ(
C:‫اﻟﻔﺎراد‬ ‫ﺑﻮﺣﺪة‬)F(،d:‫ﻣﺘﺮ‬ ‫ﺑﻮﺣﺪة‬)m(،A:‫ﺑﻮﺣﺪة‬)m2
. (
‫ﻛﺬﻟﻚ‬:
‫ﺣﯿﺚ‬:
Ck:‫ﻋﺎزﻟﺔ‬ ‫ﻣﺎدة‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬.‫ﻧﺠﺪ‬ ‫اﻋﻼه‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻣﻦ‬:
♦‫ان‬ ‫ﻧﺠﺪ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫ﻋﻠﯿﮫﺎ‬ ‫ﺗﻌﺘﻤﺪ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻌﻮاﻣﻞ‬ ‫ﻣﻦ‬:
2
1
1
2
d
d
C
C
d
1
C =⇒αQ
1
2
1
2
A
A
C
C
AC =⇒αQ
d
A
C οε=
d
A
kCk
οε
=
CK=k C
‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﻮاء‬‫اﻟﮭ‬ ‫او‬ ‫ﺮاغ‬‫اﻟﻔ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺑﺪﻻ‬ ‫ﻛﮭﺮﺑﺎﺋﯿﺎ‬ ‫ﻋﺎزﻟﺔ‬ ‫ﻣﺎدة‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫ﯾﻔﺼﻞ‬ ‫ﻋﻨﺪﻣﺎ‬
‫ﻋﺰﻟﮭﺎ‬K.
‫اﻟﮭﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫ﯾﻔﺼﻞ‬ ‫ﻋﻨﺪﻣﺎ‬
‫اﻟﺒﻌﺪ‬ ‫ﺑﺜﺒﻮت‬‫ھﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫واﻟﻌﺎزل‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬
‫ﺑﺜﺒﻮت‬‫ھﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫واﻟﻌﺎزل‬ ‫اﻟﻤﺘﻘﺎﺑﻠﺔ‬ ‫اﻟﺴﻄﺤﯿﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬

9. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-10-
‫س‬/‫ﺼﻔﯿﺤﺘﻲ‬ ‫ﻟ‬ ‫ﺔ‬ ‫اﻟﻤﺘﻘﺎﺑﻠ‬ ‫ﺴﻄﺤﺔ‬ ‫اﻟ‬ ‫ﺴﺎﺣﺔ‬ ‫اﻟﻤ‬ ‫ﻌﻒ‬ ‫ﺿ‬ ‫ﺪاھﻤﺎ‬ ‫اﺣ‬ ‫ﺼﻔﯿﺤﺘﻲ‬ ‫ﻟ‬ ‫ﺔ‬ ‫اﻟﻤﺘﻘﺎﺑﻠ‬ ‫ﺴﻄﺤﯿﺔ‬ ‫اﻟ‬ ‫ﺴﺎﺣﺔ‬ ‫اﻟﻤ‬ ‫ﺴﻌﺘﺎن‬ ‫ﻣﺘ‬ ‫ﺪﯾﻚ‬ ‫ﻟ‬
‫ھﻮاء؟‬ ‫او‬ ‫ﻓﺮاغ‬ ‫اﻟﻌﺎزل‬ ‫ﻛﺎن‬ ‫اذا‬ ‫ﺳﻌﺘﯿﮭﺎ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻨﺴﺒﺔ‬ ‫ﻣﺎ‬ ‫اﻻﺧﺮى‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫ﻧﺼﻒ‬ ‫ﺻﻔﯿﺤﺘﯿﮭﺎ‬ ‫ﺑﯿﻦ‬ ‫واﻟﺒﻌﺪ‬ ‫اﻻﺧﺮى‬
‫ج‬/
4
C
C
d
2
1
A
dA2
C
C
d
2
1
d,A2A,
dA
dA
C
C
d
A
d
A
C
C
2
1
22
22
2
1
2121
12
21
2
1
2
2
1
1
2
1
=⇒
×
=∴
===⇒
ε
ε
=
ο
ο
Q
‫ﻣﻼﺣﻈﺎﺕ‬/
1-‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬‫اﻟﺘﺎﻟﯿﺔ‬:
V
Q
C
∆
=‫أن‬ ‫ﻧﺠﺪ‬:
a(‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺐ‬‫ﺗﺘﻨﺎﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﻣﻦ‬ ‫اي‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﺸﺤﻨﺔ‬)‫ﺪ‬‫اﺣ‬ ‫ﺮ‬‫ﺑﺘﻐﯿ‬ ‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﺮت‬‫ﺗﻐﯿ‬ ‫ﻮ‬‫ﻟ‬ ‫ﺎ‬‫ﻓﯿﻤ‬
‫ﻋﻮاﻣﻠﮭﺎ‬(‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺜﺒﺖ‬ ‫ﺣﯿﺚ‬‫ﺑﺎﻟﺒﻄﺎرﯾﺔ‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬(
‫ان‬ ‫أي‬:CQα)‫ﺑﺜﺒﻮت‬∆V(
b(‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺴﯿﺎ‬‫ﻋﻜ‬ ‫ﺐ‬‫ﯾﺘﻨﺎﺳ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬)‫ﺪ‬‫اﺣ‬ ‫ﺮ‬‫ﺑﺘﻐﯿ‬ ‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﺮت‬‫ﺗﻐﯿ‬ ‫ﻮ‬‫ﻟ‬ ‫ﺎ‬‫ﻓﯿﻤ‬
‫ﻋﻮاﻣﻠﮭﺎ‬(‫ﺷﺤﻨﺘﮭﺎ‬ ‫ﺛﺒﻮت‬ ‫ﻋﻨﺪ‬)‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﻋﻦ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺗﻔﺼﻞ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺜﺒﺖ‬ ‫ﺣﯿﺚ‬(‫ان‬ ‫أي‬:
C
1
V α∆)‫ﺑﺜﺒﻮت‬Q.(
c(‫ﺗﺘﻐﯿﺮ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫ﺑﺎن‬ ‫ﺗﺬﻛﺮ‬‫ﻋﻠﯿﮭﺎ‬ ‫اﻟﻤﺆﺛﺮ‬ ‫اﻟﻌﻮاﻣﻞ‬ ‫اﺣﺪ‬ ‫ﺑﺘﻐﯿﺮ‬)‫ﯿﻦ‬‫ﺑ‬ ‫اﻟﺒﻌﺪ‬ ‫او‬ ‫اﻟﻤﺘﻮازﯾﺘﯿﻦ‬ ‫ﻟﻠﺼﻔﯿﺤﺘﯿﻦ‬ ‫اﻟﻤﺘﻘﺎﺑﻠﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬
‫اﻟﻔﺮاغ‬ ‫او‬ ‫اﻟﮭﻮاء‬ ‫ﻣﻦ‬ ‫ﺑﺪﻻ‬ ‫ﺻﻔﯿﺤﺘﯿﮭﺎ‬ ‫ﺑﯿﻦ‬ ‫ﻋﺎزﻟﺔ‬ ‫ﻣﺎدة‬ ‫إدﺧﺎل‬ ‫او‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬. (
d(‫اﻟﻜﮭﺮﺑﺎﺋ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬‫ﺪ‬‫ﻋﻨ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﻦ‬‫ﻣ‬ ‫أي‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫ﯾﺘﻨﺎﺳﺐ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫ﻲ‬
‫اﻟﺴﻌﺔ‬ ‫ﺛﺒﻮت‬.‫ان‬ ‫أي‬
∆V α Q)‫ﺑﺜﺒﻮت‬(C
2-‫واﺣﺪ‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫داﺋﻤﺎ‬ ‫ﯾﻜﻮن‬ ‫اﻻﺧﺮى‬ ‫اﻟﻌﺎزﻟﺔ‬ ‫ﻟﻠﻤﻮاد‬ ‫ﺑﯿﻨﻤﺎ‬ ‫واﺣﺪ‬ ‫ﯾﺴﺎوي‬ ‫اﻟﮭﻮاء‬ ‫او‬ ‫ﻟﻠﻔﺮاغ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬.
3-‫ﺑﺸﺤﻨﺔ‬ ‫اﻟﻤﻘﺼﻮد‬‫ﺻﻔﯿﺤﺘﯿﮭﺎ‬ ‫ﻣﻦ‬ ‫أي‬ ‫ﺷﺤﻨﺔ‬ ‫ھﻲ‬ ‫اﻟﻤﺘﺴﻌﺔ‬)‫اﻟﺴﺎﻟﺒﺔ‬ ‫او‬ ‫اﻟﻤﻮﺟﺒﺔ‬(‫اﻟﻜﻠﯿﺔ‬ ‫ﺷﺤﻨﺘﮭﺎ‬ ‫وﻟﯿﺲ‬.
4-‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫ﯾﺴﺎوي‬ ‫ﺳﻤﻜﮫ‬ ‫ﻓﺎن‬ ‫ﺗﻤﺎﻣﺎ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺤﯿﺰ‬ ‫اﻟﻌﺎزل‬ ‫ﯾﻤﻸ‬ ‫ﻋﻨﺪﻣﺎ‬.
‫اﻟﻤﻨﻔﺮدة‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻗﻮاﻧﻴﻦ‬ ‫ﺧﻼﺻﺔ‬:
‫اﻟﻌﺎزل‬ ‫ﻗﺒﻞ‬:
,
‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬:
,
d
V
E k
k
∆
=d
A
kCor
V
Q
C k
k
k
k οε=
∆
=
C
Q
.
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE
2
2
=∆=∆=
d
V
E
∆
=
d
A
Cor
V
Q
C οε=
∆
=

10. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-11-
+ -
∆Vtotal
C1
C2
n21total V.........VVV ∆=∆=∆=∆
n21total Q.........QQQ ++=
n21eq C.........CCC ++=
‫اﻟﻌﻼﻗﺎت‬:
‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬‫اﻟﻤﺼﺪ‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬‫ر‬
CkCk =CkCk =
QkQk =QQk =
VVk ∆=∆
k
V
Vk
∆
=∆
EEk =
k
E
Ek =
PEkPEk =
k
PE
PEk =
‫ﺍﳌ‬ ‫ﺭﺑﻂ‬‫ﺘﺴﻌﺎﺕ‬)‫ﺗﻮﺍﱄ‬ ، ‫ﺗﻮﺍﺯﻱ‬(:
‫أوﻻ‬:‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫رﺑﻂ‬:
‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬‫رﺑﻂ‬n‫ﻓﺎن‬ ‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬:
`1-‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﻊ‬‫ﺟﻤﯿ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺴﺎوي‬‫ﻣﺘ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﻓﺮق‬)‫ﺖ‬‫ﺛﺎﺑ‬(‫ﺪ‬‫ﺟﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺴﺎوي‬‫وﯾ‬
‫اﻟﺒﻄﺎرﯾﺔ‬)‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬(‫ان‬ ‫أي‬:
2-‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻋﻠﻰ‬ ‫اﻟﺸﺤﻨﺎت‬ ‫ﻣﺠﻤﻮع‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬)‫ﺗﺘﻮزع‬(‫ان‬ ‫أي‬:
3-‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬)Ceq(‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﺳﻌﺎت‬ ‫ﻣﺠﻤﻮع‬ ‫ﺗﺴﺎوي‬‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻓﻲ‬ ‫ﺳﻌﺔ‬ ‫اﻛﺒﺮ‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫وﺗﻜﻮن‬‫ان‬ ‫أي‬:
4-‫ﺔ‬‫ﻣﺘﻤﺎﺛﻠ‬ ‫ﺴﻌﺎت‬‫ﻣﺘ‬ ‫ﻟﻤﺠﻤﻮﻋﺔ‬ ‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬)‫اي‬‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﺴﺎوﯾﺔ‬‫ﻣﺘ‬(‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﺪد‬‫ﻋ‬ ‫ﺴﺎوي‬‫ﺗ‬)n(‫ﺎ‬‫ﻣﻨﮭ‬ ‫ﺪة‬‫واﺣ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﻲ‬‫ﻓ‬.
‫ان‬ ‫أي‬:
5-‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ﻮع‬‫ﻣﺠﻤ‬ ‫ﺴﺎوي‬‫ﺗ‬ ‫ﻮازي‬‫اﻟﺘ‬ ‫ﺔ‬‫ﻟﻤﺠﻤﻮﻋ‬ ‫ﺔ‬‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬
‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻛﻞ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬.‫ان‬ ‫أي‬:
n21T PE.........PEPEPE ++=
CnCeq =
k
2
k
k
2
kkkkkk
C
Q
.
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE =∆=∆=
‫ﻣﺮ‬ ‫ﻣﺘﺴﻌﺎت‬ ‫ﻟﻤﺠﻤﻮﻋﺔ‬ ‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻹﯾﺠﺎد‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ھﺬه‬ ‫ﺗﺴﺘﺨﺪم‬‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬ ‫ﺑﻮطﺔ‬

11. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-12-
+ -
C1 C2
∆Vtotal
n21total V.........VVV ∆+∆+∆=∆
n21total Q.........QQQ ===
‫س‬/‫اﻟﺴﻌﺔ‬ ‫ﻟﺤﺴﺎب‬ ‫ﻋﻼﻗﺔ‬ ‫اﺷﺘﻖ‬‫اﻟﻤﻜﺎﻓﺌﺔ‬)Ceq(‫ﻟ‬‫ﻤ‬‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺮﺑﻮطﺔ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﺠﻤﻮﻋﺔ‬.
‫ج‬/
21eq21eq21eq
21total
2211totaleq21total
CCCV).CC(V.CV.CV.CV.C
VVVV
V.CV.CV.CQQQ
+=⇒∆+=∆⇒∆+∆=∆∴
∆=∆=∆=∆
∆+∆=∆⇒+=
Q
‫ﺗﻨﻮﯾﮫ‬/
‫ﻮازي‬‫اﻟﺘ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺴﻌﺘﯿﻦ‬‫ﻣﺘ‬ ‫ﻂ‬‫رﺑ‬ ‫ﺪ‬‫ﻋﻨ‬)‫ﺼﺪر‬ ‫ﻣ‬ ‫ﺪون‬‫ﺑ‬(‫ﺴﻌﺘﯿﻦ‬‫اﻟﻤﺘ‬ ‫ﻮن‬‫ﺗﻜ‬ ‫ان‬ ‫ﻰ‬‫ﻋﻠ‬‫ﺪ‬ ‫ﺟﮭ‬ ‫ﺮق‬‫ﻟﻔ‬ ‫ﺴﺒﻘﺎ‬‫ﻣ‬ ‫ﺸﺤﻮﻧﺘﯿﻦ‬‫ﻣ‬
‫ﻣﺸﺤﻮﻧﺔ‬ ‫ﻏﯿﺮ‬ ‫واﻻﺧﺮى‬ ‫ﻣﺸﺤﻮﻧﺔ‬ ‫اﺣﺪاھﻤﺎ‬ ‫او‬ ‫ﻣﺨﺘﻠﻒ‬‫اﻟﺘﺎﻟﻲ‬ ‫ﺑﺎﻟﺸﻜﻞ‬ ‫ﺗﻜﻮن‬ ‫اﻟﺤﻞ‬ ‫ﺧﻄﻮات‬ ‫ﻓﺎن‬:
1-‫ﻟﻢ‬ ‫ان‬ ‫اﻟﺘﻮﺻﯿﻞ‬ ‫ﻗﺒﻞ‬ ‫اﻟﻤﺘﺴﻌﺘﯿﻦ‬ ‫ﻣﻦ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫ﻧﺠﺪ‬‫اﻟﻘﺎﻧﻮن‬ ‫ﻣﻦ‬ ‫ﻣﻮﺟﻮدة‬ ‫ﺗﻜﻦ‬:
222
111
V.CQ
V.CQ
∆=
∆=
2-‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺤﺼﻮل‬ ‫اﻟﺘﻮازي‬ ‫ﺧﻮاص‬ ‫ﻣﻦ‬ ‫اﻟﻤﺘﺴﻌﺘﯿﻦ‬ ‫ﺷﺤﻨﺔ‬ ‫ﻧﺠﻤﻊ‬:
21T QQQ +=
3-‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺤﺼﻮل‬ ‫اﻟﻤﺘﺴﻌﺘﯿﻦ‬ ‫ﺳﻌﺔ‬ ‫ﻧﺠﻤﻊ‬:
21eq CCC +=
4-‫ﯾ‬ ‫واﻟﺬي‬ ‫ﻟﻠﻤﺘﺴﻌﺘﯿﻦ‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﺴﺘﺨﺮج‬‫ﺗﻮازي‬ ‫اﻟﺮﺑﻂ‬ ‫ﻟﻜﻮن‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺟﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺴﺎوي‬:
21
eq
T
T VV
C
Q
V ∆=∆==∆
5-‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫ﺑﺎﻟﻘﺎﻧﻮن‬ ‫اﻟﻤﺘﺴﻌﺘﯿﻦ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﻮزﯾﻊ‬ ‫ﻧﻌﯿﺪ‬:
222
111
V.CQ
V.CQ
∆=
∆=
v‫اﻟﺘﻮﺻﯿﻞ‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﺘﻮﺻﯿﻞ‬ ‫ﻗﺒﻞ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﻜﻮن‬ ‫ان‬ ‫ﯾﺠﺐ‬ ‫اﻟﺤﻞ‬ ‫ﺻﺤﺔ‬ ‫ﻣﻦ‬ ‫ﻟﻠﺘﺎﻛﺪ‬.
v‫ھﺬه‬‫ﺑﻌﺾ‬ ‫ﻣﻊ‬ ‫اﻟﻤﺘﻤﺎﺛﻠﺔ‬ ‫اﻟﺼﻔﺎﺋﺢ‬ ‫رﺑﻂ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬ ‫ﺗﺴﺘﺨﺪم‬ ‫اﻟﺨﻄﻮات‬)‫ﺔ‬‫ﻟﻠﻤﻮﺟﺒ‬ ‫اﻟﻤﻮﺟﺒﺔ‬ ‫اﻟﺼﻔﯿﺤﺔ‬ ‫أي‬‫ﺴﺎﻟﺒﺔ‬‫اﻟ‬ ‫ﺼﻔﯿﺤﺔ‬‫واﻟ‬
‫ﻟﻠﺴﺎﻟﺒﺔ‬. (
v‫ﺔ‬‫اﻟﺜﺎﻧﯿ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻦ‬‫ﻣ‬ ‫ﻔﯿﺤﺔ‬‫ﺻ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫ﻣﻊ‬ ‫اﻻوﻟﻰ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻣﻦ‬ ‫ﺻﻔﯿﺤﺔ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫ﻓﺘﺘﻌﺎدل‬ ‫اﻟﻤﺨﺘﻠﻔﺔ‬ ‫اﻟﺼﻔﺎﺋﺢ‬ ‫رﺑﻂ‬ ‫ﻋﻨﺪ‬
‫ﺗﺴﺎ‬ ‫اﻟﺘﻮﺻﯿﻞ‬ ‫ﺑﻌﺪ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫وﺗﺼﺒﺢ‬‫ﺻﻔﺮ‬ ‫وي‬‫ﻮ‬‫ﻟ‬ ‫ﺎ‬‫اﻣ‬ ‫ﺴﺎوﯾﺔ‬‫ﻣﺘ‬ ‫ﺴﻌﺘﯿﻦ‬‫اﻟﻤﺘ‬ ‫ﺤﻨﺔ‬‫ﺷ‬ ‫ﺖ‬‫ﻛﺎﻧ‬ ‫ﻮ‬‫ﻟ‬ ‫ﺎ‬‫ﻓﯿﻤ‬
‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺼﻮل‬‫ﻟﻠﺤ‬ ‫ﺴﻌﺘﯿﻦ‬‫اﻟﻤﺘ‬ ‫ﺤﻨﺔ‬‫ﺷ‬ ‫ﻧﺠﻤﻊ‬ ‫ان‬ ‫ﻣﻦ‬ ‫وﺑﺪﻻ‬ ‫اﻋﻼه‬ ‫اﻟﻘﻮاﻋﺪ‬ ‫ﻧﻔﺲ‬ ‫ﻓﻨﺘﺒﻊ‬ ‫ﻣﺨﺘﻠﻔﺔ‬ ‫اﻟﻤﺘﺴﻌﺘﯿﻦ‬ ‫ﺷﺤﻨﺔ‬ ‫ﻛﺎﻧﺖ‬
‫ﻧﻄﺮﺣﮭﻤﺎ‬ ‫اﻟﻜﻠﯿﺔ‬.
‫ﺛﺎﻧﯿﺎ‬:‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫رﺑﻂ‬:
‫رﺑﻂ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬n‫ﻓﺎن‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬:
1-‫ﻣﻘﺪار‬‫اﻟ‬ ‫ﺟﻤﯿﻊ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺘﺴﺎوي‬ ‫اﻟﺸﺤﻨﺔ‬‫ان‬ ‫أي‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫وﯾﺴﺎوي‬ ‫ﻤﺘﺴﻌﺎت‬:
2-‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬)∆Vtotal(‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮوق‬ ‫ﻣﺠﻤﻮع‬ ‫ﯾﺴﺎوي‬)‫ﯾﺘﻮزع‬(‫ان‬ ‫أي‬:

12. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-13-
n21eq C
1
.........
C
1
C
1
C
1
++=
3-‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻣﻘﻠﻮب‬‫ﻟﻠﻤﺠﻤﻮﻋﺔ‬‫ﯾﺴﺎوي‬‫ﺳﻌﺎت‬ ‫ﻣﻘﻠﻮب‬ ‫ﻣﺠﻤﻮع‬‫ﺔ‬‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﺪار‬‫ﻣﻘ‬ ‫ﺎن‬‫ﻓ‬ ‫وﺑﺎﻟﺘﺎﻟﻲ‬ ‫اﻟﻤﺘﺴﻌﺎت‬)Ceq(
‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻓﻲ‬ ‫ﺳﻌﺔ‬ ‫اﺻﻐﺮ‬ ‫ﻣﻦ‬ ‫اﺻﻐﺮ‬ ‫وﯾﻜﻮن‬ ‫ﯾﻘﻞ‬‫ان‬ ‫أي‬:
♦‫ﻓﻲ‬‫اﻟﻤﻜﺎﻓﺌـﺔ‬ ‫اﻟـﺴﻌﺔ‬ ‫ﻧﺤـﺴﺐ‬ ‫أن‬ ‫ﻳﻤﻜـﻦ‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻓﻘﻂ‬ ‫ﻣﺘﺴﻌﺘﻴﻦ‬ ‫رﺑﻂ‬ ‫ﺣﺎﻟﺔ‬‫ﻟﻬﻤـﺎ‬‫ﻣـﻦ‬‫اﻟـﺴﻌﺘﻴﻦ‬ ‫ﺿـﺮب‬ ‫ﺣﺎﺻـﻞ‬
‫اﻟﺴﻌﺘﻴﻦ‬ ‫ﻣﺠﻤﻮع‬ ‫ﻋﻠﻰ‬‫وﻓﻘﺎ‬‫ﻟ‬‫اﻻ‬ ‫ﻠﻌﻼﻗﺔ‬‫ﺗﻴﺔ‬:
4-‫ﻟﻤﺠﻤﻮ‬ ‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬‫ﻣﺘﻤﺎﺛﻠﺔ‬ ‫ﻣﺘﺴﻌﺎت‬ ‫ﻋﺔ‬)‫اﻟﺴﻌﺔ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫اي‬(‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﺪد‬‫ﻋ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫واﺣﺪ‬ ‫ﺳﻌﺔ‬ ‫ﺗﺴﺎوي‬
)n. (‫ان‬ ‫أي‬:
5-‫اﻟﻄ‬ ‫ﻮع‬ ‫ﻣﺠﻤ‬ ‫ﺴﺎوي‬‫ﺗ‬ ‫ﻮاﻟﻲ‬ ‫اﻟﺘ‬ ‫ﺔ‬ ‫ﻟﻤﺠﻤﻮﻋ‬ ‫ﺔ‬‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬ ‫اﻟﻤﺠ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬ ‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬‫ﺔ‬ ‫ﺎﻗ‬
‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻛﻞ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬.‫ان‬ ‫أي‬:
‫س‬/‫اﺷﺘﻖ‬‫ﻟﺤﺴﺎب‬ ‫ﻋﻼﻗﺔ‬‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬)Ceq(‫ﻟ‬‫ﻤ‬‫ﺠﻤﻮﻋﺔ‬‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺮﺑﻮطﺔ‬.
‫ج‬/
21eq21eq21eq
21total
2
2
1
1
eq
total
21total
C
1
C
1
C
1
)
C
1
C
1
.(Q
C
Q
C
Q
C
Q
C
Q
QQQQ
C
Q
C
Q
C
Q
VVV
+=⇒+=⇒+=∴
===
+=⇒∆+∆=∆
Q
‫ﺛﺎﻟﺜﺎ‬:‫اﻟﻤﺨﺘﻠﻂ‬ ‫اﻟﺮﺑﻂ‬:
♦‫واﻟﺘﻮاﻟﻲ‬ ‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫رﺑﻂ‬ ‫ﻋﻨﺪ‬)‫رﺑﻂ‬‫ﻣﺨﺘﻠﻂ‬(‫ﻣﻌـﺎ‬ ‫واﻟﺘﻮاﻟﻲ‬ ‫اﻟﺘﻮازي‬ ‫ﺧﻮاص‬ ‫ﺗﻄﺒﻴﻖ‬ ‫ﻓﻴﺠﺐ‬‫ﻓﻠـﻮ‬
‫اﻟﺘ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺘﺴﻌﺘﺎن‬ ‫ﻣﺜﻼ‬ ‫ﻛﺎﻧﺖ‬‫ﻣﻜﺎﻓﺌـﺔ‬ ‫ﻣﺘـﺴﻌﺔ‬ ‫اوﻻ‬ ‫ﻧـﺴﺘﺨﺮج‬ ‫اﻟﺘـﻮاﻟﻲ‬ ‫ﻋﻠـﻰ‬ ‫ﺛﺎﻟﺜﺔ‬ ‫وﻣﻊ‬ ‫ﻮازي‬‫ﻟ‬‫اﻟ‬ ‫ﻤﺠﻤﻮﻋـﺔ‬‫ﺘـﻮازي‬‫ﻓﻴﺘﺤـﻮل‬
‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻧﺠﺪ‬ ‫ﺛﻢ‬ ‫ﺗﻮاﻟﻲ‬ ‫اﻟﻰ‬ ‫اﻟﺮﺑﻂ‬)‫ﺑﺎﻟﻤﻘﻠﻮب‬.(‫ﻣـﻊ‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺘﺴﻌﺘﺎن‬ ‫ﻣﺜﻼ‬ ‫ﻛﺎﻧﺖ‬ ‫وﻟﻮ‬‫اﻟﺘـﻮازي‬ ‫ﻋﻠـﻰ‬ ‫ﺛﺎﻟﺜـﺔ‬
‫ﻧﺴ‬‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫اوﻻ‬ ‫ﺘﺨﺮج‬‫ﻟ‬‫اﻟ‬ ‫ﻤﺠﻤﻮﻋﺔ‬‫ﺘﻮاﻟﻲ‬‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻧﺠﺪ‬ ‫ﺛﻢ‬ ‫ﺗﻮازي‬ ‫اﻟﻰ‬ ‫اﻟﺮﺑﻂ‬ ‫ﻓﻴﺘﺤﻮل‬)‫ﺑﺎﻟﻤﺠﻤﻮع‬.(
♦‫ﻣﺮﺑﻮﻃﺔ‬ ‫ﻣﺘﺴﻌﺎت‬ ‫ﻟﻤﺠﻤﻮﻋﺔ‬ ‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬ ‫ﺗﻜﻮن‬‫ﻣﺨﺘﻠﻂ‬ ‫رﺑﻂ‬ ‫او‬ ‫ﺗﻮاﻟﻲ‬ ‫رﺑﻂ‬)‫ﺗﻮازي‬‫و‬‫ﺗﻮاﻟﻲ‬(‫اﻟـﺴﻌﺔ‬ ‫ﻣﻦ‬ ‫اﺻﻐﺮ‬ ‫ﻫﻲ‬
‫ﺗﻮازي‬ ‫رﺑﻂ‬ ‫ﻣﺮﺑﻮﻃﺔ‬ ‫ﻣﺘﺴﻌﺎت‬ ‫ﻟﻤﺠﻤﻮﻋﺔ‬ ‫اﻟﻤﻜﺎﻓﺌﺔ‬.
n21T PE.........PEPEPE ++=
n
C
Ceq =
21
21
eq
CC
C.C
C
+
=
‫اﻟﻤﻜﺎﻓ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻹﯾﺠﺎد‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ھﺬه‬ ‫ﺗﺴﺘﺨﺪم‬‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺮﺑﻮطﺔ‬ ‫ﻣﺘﺴﻌﺎت‬ ‫ﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﺌﺔ‬

13. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-14-
‫ﺻﻔ‬ ‫ﺑﻴﻦ‬ ‫ﻋﺎزل‬ ‫إدﺧﺎل‬‫ﻣﺘﺴﻌﺔ‬ ‫ﻴﺤﺘﻲ‬‫واﺣﺪة‬‫ﻣﺘﻮاﻟﻴﺔ‬ ‫او‬ ‫ﻣﺘﻮازﻳﺔ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﻣﻦ‬ ‫اﻛﺜﺮ‬ ‫او‬:
‫ﻋﺰﻟﮭﺎ‬ ‫ﺛﺎﺑﺖ‬ ‫ﻋﺎزﻟﺔ‬ ‫ﻣﺎدة‬ ‫إدﺧﺎل‬ ‫ﻋﻨﺪ‬)k(‫ﻓﺎن‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫اﻛﺜﺮ‬ ‫او‬ ‫واﺣﺪة‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬:
1-‫اﻟﻌﺎزل‬ ‫إدﺧﺎل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻤﻜﺎﻓﺌﺔ‬ ‫اﻟﺴﻌﺔ‬)Ceqk(‫ﺾ‬‫وﺑﻐ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﺎ‬‫ﻋﻠﯿﮭ‬ ‫ﻞ‬‫ادﺧ‬ ‫ﻲ‬‫اﻟﺘ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ﺎدة‬‫زﯾ‬ ‫ﺴﺒﺐ‬‫ﺑ‬ ‫ﺰداد‬‫ﺗ‬ ‫ﺳﻮف‬
‫اﻟﻨﻈ‬‫ﺮ‬‫ا‬ ‫ﻛﻮن‬ ‫ﻋﻦ‬‫ﻮاﻟﻲ‬‫ﺗ‬ ‫او‬ ‫ﻮازي‬‫ﺗ‬ ‫ﺮﺑﻂ‬‫اﻟ‬ ‫ﻮن‬‫اوﻛ‬ ‫ﺼﻠﺔ‬‫ﻣﻨﻔ‬ ‫او‬ ‫ﺼﻠﺔ‬‫ﻣﺘ‬ ‫ﻟﻤﺠﻤﻮﻋﺔ‬‫ﺼﺒﺢ‬‫وﺗ‬)Ceqk > Ceq(‫ﻦ‬‫ﻣ‬ ‫ﺎ‬‫اﻣ‬ ‫ﺴﺐ‬‫وﺗﺤ‬
‫اﻟﻘﺎﻧﻮن‬)
Tk
Tk
eqk
V
Q
C
∆
=(‫اﻟﺮﺑﻂ‬ ‫ﺧﻮاص‬ ‫ﻣﻦ‬ ‫او‬)‫اﻟﺘﻮاﻟﻲ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬ ‫ﺑﺎﻟﻤﻘﻠﻮب‬ ‫او‬ ‫اﻟﺘﻮازي‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬ ‫ﺑﺎﻟﻤﺠﻤﻮع‬.(
2-‫ﺎزل‬‫اﻟﻌ‬ ‫ﻮد‬‫ﺑﻮﺟ‬ ‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬)QTk(‫ﺰداد‬‫ﺗ‬)QTk > QT(‫اﻟﺠ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺖ‬‫وﯾﺜﺒ‬‫ﺪ‬‫ﺑﻌ‬ ‫ﻲ‬‫اﻟﻜﻠ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ان‬ ‫أي‬ ‫ﻲ‬‫اﻟﻜﻠ‬ ‫ﺪ‬‫ﮭ‬
‫ﺎزل‬ ‫اﻟﻌ‬ ‫ﻞ‬‫ﻗﺒ‬ ‫ﻲ‬ ‫اﻟﻜﻠ‬ ‫ﺪ‬ ‫اﻟﺠﮭ‬ ‫ﺮق‬ ‫ﻓ‬ ‫ﺴﺎوي‬ ‫ﯾ‬ ‫ﺎزل‬ ‫اﻟﻌ‬)TTk VV ∆=∆(‫ﺖ‬ ‫ﺗﺜﺒ‬ ‫او‬ ‫ﺔ‬ ‫ﺑﺎﻟﺒﻄﺎرﯾ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﺔ‬ ‫اﻟﻤﺠﻤﻮﻋ‬ ‫ﻮن‬ ‫ﺗﻜ‬ ‫ﺪﻣﺎ‬ ‫ﻋﻨ‬
‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬‫اﻟﻌﺎزل‬ ‫ﻗﺒﻞ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ان‬ ‫أي‬)TTk QQ =(‫ﺮق‬‫ﻓ‬ ‫ﻞ‬‫وﯾﻘ‬‫ﻲ‬‫اﻟﻜﻠ‬ ‫ﺪ‬‫اﻟﺠﮭ‬
)TTk VV ∆<∆(‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬.
3-‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺸﺤﻨﺔ‬‫واﻟ‬ ‫ﺗﻮازي‬ ‫اﻟﺮﺑﻂ‬ ‫ﻛﺎن‬ ‫اذا‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺟﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺴﺎوي‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫اﻟﻌﺎزل‬ ‫إدﺧﺎل‬ ‫ﺑﻌﺪ‬
‫اﻟﻨ‬ ‫ﺾ‬‫وﺑﻐ‬ ‫ﻮاﻟﻲ‬‫ﺗ‬ ‫ﺮﺑﻂ‬‫اﻟ‬ ‫ﺎن‬‫ﻛ‬ ‫اذا‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬‫ام‬ ‫ﺼﻠﺔ‬‫ﻣﺘ‬ ‫ﺔ‬‫اﻟﻤﺠﻤﻮﻋ‬ ‫ﻮن‬‫ﻛ‬ ‫ﻦ‬‫ﻋ‬ ‫ﺮ‬‫ﻈ‬
‫ﻣﻨﻔﺼﻠﺔ‬.
‫ان‬ ‫أي‬:
n21Tk V........VVV ∆=∆=∆=∆ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫ام‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻛﻮن‬ ‫ﻋﻦ‬ ‫اﻟﻨﻈﺮ‬ ‫وﺑﻐﺾ‬ ‫ﻟﻠﺘﻮازي‬
or
n21Tk Q...........QQQ === ‫ﻣﻨﻔﺼﻠﺔ‬ ‫ام‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻛﻮن‬ ‫ﻋﻦ‬ ‫اﻟﻨﻈﺮ‬ ‫وﺑﻐﺾ‬ ‫ﻟﻠﺘﻮاﻟﻲ‬
4-‫اﻟﻌ‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺜﺒﺖ‬ ‫اﻟﺤﺎﻻت‬ ‫ﻣﻦ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬‫ﺔ‬‫اﻟﻤﺠﻤﻮﻋ‬ ‫ﺖ‬‫ﻛﺎﻧ‬ ‫اذا‬ ‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺴﻌﺔ‬‫ﻣﺘ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫ﺗﺴﺎوي‬ ‫ﺛﻢ‬ ‫ﺎزل‬
‫ﺴﺎوي‬‫ﺗ‬ ‫ﻢ‬‫ﺛ‬ ‫ﻦ‬‫وﻣ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﺎل‬‫إدﺧ‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺰداد‬ ‫اﺧﺮى‬ ‫ﺣﺎﻟﺔ‬ ‫وﻓﻲ‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺮﺑﻂ‬ ‫وﻛﺎن‬ ‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬
‫ﺗﻮاﻟﻲ‬ ‫اﻟﺮﺑﻂ‬ ‫وﻛﺎن‬ ‫ﺑﺎﻟﺒﻄﺎرﯾﺔ‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬.
5-‫ﻣﻦ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬‫ﺖ‬‫ﻛﺎﻧ‬ ‫اذا‬ ‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺴﻌﺔ‬‫ﻣﺘ‬ ‫ﻞ‬‫ﻛ‬ ‫ﺪ‬‫ﺟﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺴﺎوي‬‫ﯾ‬ ‫ﻢ‬‫ﺛ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﺪ‬‫ﺑﻌ‬ ‫ﻲ‬‫اﻟﻜﻠ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﯾﺜﺒﺖ‬ ‫اﻟﺤﺎﻻت‬
‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺟﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺴﺎوي‬ ‫ﺛﻢ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﻘﻞ‬ ‫اﺧﺮى‬ ‫ﺣﺎﻟﺔ‬ ‫وﻓﻲ‬ ‫ﺗﻮازي‬ ‫اﻟﺮﺑﻂ‬ ‫وﻛﺎن‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬
‫ﺗﻮازي‬ ‫اﻟﺮﺑﻂ‬ ‫وﻛﺎن‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬.
6-‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬‫اﻟﻌﻼﻗﺎت‬ ‫ﻧﺘﺠﻨﺐ‬ ‫ان‬ ‫ﻋﻠﯿﻨﺎ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫رﺑﻂ‬)Qk=kQ‫و‬
k
V
Vk
∆
=∆‫و‬
k
E
Ek =(‫ﺎ‬‫ﻟﻜﻮﻧﮭ‬
‫ﺧﺎﺻﺔ‬ ‫ﺣﺎﻻت‬ ‫ﻓﻲ‬ ‫ﺗﻄﺒﻖ‬.
‫ﺣﻞ‬ ‫ﻋﻨﺪ‬ ‫ﻟﻬﺎ‬ ‫اﻻﻟﺘﻔﺎت‬ ‫ﻳﺠﺐ‬ ‫ﻣﻼﺣﻈﺎت‬‫ﺑﻌﺾ‬‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﺴﺎﺋﻞ‬:
1-‫اﻟﻌﺎ‬ ‫ﻗﺒﻞ‬ ‫اﻟﺴﻌﺔ‬ ‫اﻟﻰ‬ ‫ﺗﻀﺎف‬ ‫اﻟﻌﺎزل‬ ‫إدﺧﺎل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻓﻲ‬ ‫اﻟﺰﯾﺎدة‬ ‫ﻣﻘﺪار‬ ‫ان‬‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺴﻌﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺤﺼﻮل‬ ‫زل‬.
2-‫ﺎزل‬‫اﻟﻌ‬ ‫ﺪ‬‫ﺑﻌ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺼﻮل‬‫ﻟﻠﺤ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﻞ‬‫ﻗﺒ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻰ‬‫اﻟ‬ ‫ﻀﺎف‬‫ﺗ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﺎل‬‫إدﺧ‬ ‫ﺪ‬‫ﺑﻌ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻓﻲ‬ ‫اﻟﺰﯾﺎدة‬ ‫ﻣﻘﺪار‬ ‫ان‬
)‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫او‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﺑﺎﻟﺸﺤﻨﺔ‬ ‫اﻟﺰﯾﺎدة‬ ‫ﺗﺤﺼﻞ‬ ‫ﺣﯿﺚ‬.(
3-‫اﻻﻧﺨﻔﺎض‬ ‫او‬ ‫اﻟﻨﻘﺼﺎن‬ ‫ﻣﻘﺪار‬ ‫ان‬‫ﻰ‬‫ﻋﻠ‬ ‫ﺼﻮل‬‫ﻟﻠﺤ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﻞ‬‫ﻗﺒ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻣﻦ‬ ‫ﯾﻄﺮح‬ ‫اﻟﻌﺎزل‬ ‫إدﺧﺎل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻓﻲ‬
‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬)‫ﻦ‬‫ﻋ‬ ‫ﺼﻠﺔ‬‫ﻣﻨﻔ‬ ‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﺔ‬‫ﻣﺠﻤﻮﻋ‬ ‫او‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻮن‬‫ﺗﻜ‬ ‫ﺪﻣﺎ‬‫ﻋﻨ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻓﻲ‬ ‫ﻧﻘﺼﺎن‬ ‫ﯾﺤﺼﻞ‬ ‫ﺣﯿﺚ‬
‫اﻟﻤﺼﺪر‬.(
‫اﻟﻤﺘﺴﻌﺔ‬ ‫وﺗﻔﺮﻳﻎ‬ ‫ﺷﺤﻦ‬:
‫اوﻻ‬:‫اﻟﺸﺤﻦ‬ ‫ﻣﺮﺣﻠﺔ‬:
a–‫اﻟﻤﻔﺘﺎح‬ ‫ﻏﻠﻖ‬ ‫ﻟﺤﻈﺔ‬
1-‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬‫اﻟﻤﻘﺎوﻣﺔ‬ ‫طﺮﻓﻲ‬ ‫ﻋﻠﻰ‬)RV∆(‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﺟﮭﺪ‬ ‫ﻓﺮق‬ ‫وﯾﺴﺎوي‬ ‫ﯾﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻋﻈﻢ‬)batteryV∆(.‫ان‬ ‫أي‬:
batteryR VV ∆=∆

14. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-15-
2-‫اﻟﺪاﺋﺮة‬ ‫ﺗﯿﺎر‬)‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺷﺤﻦ‬ ‫ﺗﯿﺎر‬(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اوم‬ ‫ﻟﻘﺎﻧﻮن‬ ‫وﻓﻘﺎ‬ ‫وﯾﺤﺴﺐ‬ ‫ﯾﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻋﻈﻢ‬:
3-‫ﺔ‬‫واﻟﻄﺎﻗ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫واﻟﻤﺠ‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬‫اﻟ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫وﻓ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬ ‫ﻦ‬‫ﻣ‬ ‫أي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬
‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬.‫ان‬ ‫أي‬:
b-‫اﻟﺸﺤﻦ‬ ‫ﻋﻤﻠﯿﺔ‬ ‫اﻛﺘﻤﺎل‬ ‫ﺑﻌﺪ‬:
1-‫طﺮﻓﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﻨﻌﺪم‬‫ﺻﻔﺮ‬ ‫ﯾﺴﺎوي‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻓﻲ‬ ‫اﻟﺘﯿﺎر‬ ‫ﯾﺠﻌﻞ‬ ‫ﻣﻤﺎ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻓﻲ‬ ‫اﻟﻤﻘﺎوﻣﺔ‬.‫ان‬ ‫أي‬:
2-‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﺟﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺴﺎوي‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬)‫ﯾﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻋﻈﻢ‬. (‫ان‬ ‫أي‬:
3-‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬‫ﻦ‬‫ﻣ‬ ‫أي‬‫اﻟ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺎﺋﻲ‬‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬‫واﻟﻤﺠ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻔﯿﺤﺘﻲ‬‫ﺻ‬‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺨﺘﺰﻧ‬ ‫ﺔ‬‫واﻟﻄﺎﻗ‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬
‫ﯾﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻋﻈﻢ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬.‫ان‬ ‫أي‬:
‫ﻣﻼﺣﻈﺔ‬/‫رﺑﻄﻬـﺎ‬ ‫ﻋﻨـﺪ‬ ‫اﻣـﺎ‬ ‫اﻟﺒﻄﺎرﻳـﺔ‬ ‫ﺟﻬﺪ‬ ‫ﻓﺮق‬ ‫ﺗﺎﺧﺬ‬ ‫اﻟﺸﺤﻦ‬ ‫ﺑﻌﺪ‬ ‫ﻓﺎﻧﻬﺎ‬ ‫وﺑﻄﺎرﻳﺔ‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﻣﻊ‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺘﺴﻌﺔ‬ ‫رﺑﻂ‬ ‫ﻋﻨﺪ‬
‫ﻣﻘﺎوﻣﺔ‬ ‫أي‬ ‫ﻣﻊ‬ ‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬‫اﻟﺪ‬ ‫ﻣﻘﺎوﻣﺎت‬ ‫ﻣﻦ‬‫اﺋﺮة‬‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﺗﻠﻚ‬ ‫ﺟﻬﺪ‬ ‫ﻓﺮق‬ ‫ﺗﺎﺧﺬ‬ ‫ﻓﺎﻧﻬﺎ‬.
‫ﺛﺎﻧﻴﺎ‬:‫اﻟ‬ ‫ﻣﺮﺣﻠﺔ‬‫ﺘﻔﺮﻳﻎ‬:
‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺗﻔﺮﯾﻎ‬ ‫ﺗﯿﺎر‬‫ﯾﺤﺴﺐ‬‫اﻟﺘﺎﻟﯿﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬:
‫ﺣﯿﺚ‬:
I:، ‫اﻟﺘﻔﺮﯾﻎ‬ ‫ﺗﯿﺎر‬R:، ‫اﻟﺪاﺋﺮة‬ ‫ﻣﻘﺎوﻣﺔ‬∆VC:‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬
C
Q
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE
d
V
E,V.CQ
2
2
CC
C
C
=∆=∆=
∆
=∆=
0I,0VR ==∆
0PE,0E,0V,0Q C ===∆=
R
V
I
battery∆
=
R
V
I C∆
=
batteryC VV ∆=∆

15. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-16-
‫ﺔ‬‫اﻟﻤﺘﻘﺎﺑﻠ‬ ‫ﺴﺎﺣﺔ‬‫اﻟﻤ‬ ‫ﺎدة‬‫زﯾ‬ ‫او‬ ‫ﻔﯿﺤﺘﯿﮭﺎ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺪ‬‫اﻟﺒﻌ‬ ‫ﺼﺎن‬‫ﻧﻘ‬ ‫او‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫ﻋﺎزل‬ ‫إدﺧﺎل‬ ‫ﺗﺄﺛﯿﺮ‬ ‫ﯾﺒﯿﻦ‬ ‫ﺟﺪول‬
‫ﺔ‬‫واﻟﻄﺎﻗ‬ ‫ﻔﯿﺤﺘﯿﮭﺎ‬‫ﺻ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫واﻟﻤﺠﺎل‬ ‫ﺻﻔﯿﺤﺘﯿﮭﺎ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺠﮭﺪ‬ ‫وﻓﺮق‬ ‫وﺷﺤﻨﺘﮭﺎ‬ ‫ﺳﻌﺘﮭﺎ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﻋﻠﻰ‬ ‫ﻟﺼﻔﯿﺤﺘﯿﮭﺎ‬
‫اﻷو‬ ‫ﺎﻟﺘﯿﻦ‬ ‫ﺣ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺼﻔﯿﺤﺘﯿﻦ‬ ‫اﻟ‬ ‫ﯿﻦ‬ ‫ﺑ‬ ‫ﺎﺋﻲ‬ ‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬ ‫اﻟﻤﺠ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺔ‬ ‫اﻟﻤﺨﺘﺰﻧ‬‫ﻦ‬ ‫ﻋ‬ ‫ﺼﻠﺔ‬ ‫ﻣﻨﻔ‬ ‫ﺔ‬ ‫واﻟﺜﺎﻧﯿ‬ ‫ﺼﺪر‬ ‫ﺑﺎﻟﻤ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﻰ‬ ‫ﻟ‬
‫اﻟﻤﺼﺪر‬.
‫ﲟﺼﺪﺭ‬ ‫ﻣﺘﺼﻠﺔ‬ ‫ﺍﳌﺘﺴﻌﺔ‬‫ﺍﳌﺼﺪﺭ‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫ﺍﳌﺘﺴﻌﺔ‬
‫ﺻﻔﻴﺤﺘﻴﻬﺎ‬ ‫ﺑﲔ‬ ‫ﻋﺎﺯﻟﺔ‬ ‫ﻣﺎﺩﺓ‬ ‫ﺇﺩﺧﺎﻝ‬
1‫اﻟﺴﻌﺔ‬:‫ﻻن‬ ‫ﺗﺰداد‬CK = K C‫اﻟﺴﻌﺔ‬:‫ﻻن‬ ‫ﺗﺰداد‬CK = K C
2
‫اﻟﺸﺤﻨﺔ‬:‫ﺗﺰداد‬ ‫اﻟﺴﻌﺔ‬ ‫ﻻن‬ ‫ﺗﺰداد‬)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)∆V(
‫اﻟﺸﺤﻨﺔ‬:‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻻن‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﺗﺒﻘﻰ‬
3‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬:‫اﻟﻤﺼﺪر‬ ‫ﻟﻮﺟﻮد‬ ‫ﺛﺎﺑﺖ‬ ‫ﯾﺒﻘﻰ‬
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬:‫ﺗﺰداد‬ ‫اﻟﺴﻌﺔ‬ ‫ﻻن‬ ‫ﯾﻘﻞ‬)‫ﻋﻜﺴﻲ‬ ‫ﺗﻨﺎﺳﺐ‬(
‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬)Q(
4
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬:‫واﻟﺒﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻟﺜﺒﻮت‬ ‫ﺛﺎﺑﺖ‬
‫ﺣﯿﺚ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬:
d
V
E
∆
=
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬:‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﻘﺼﺎن‬ ‫ﺑﺴﺒﺐ‬ ‫ﯾﻘﻞ‬
)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫ﺑﺜﺒﻮت‬)d(
5
‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬:‫اﻟﺸﺤﻨﺔ‬ ‫زﯾﺎدة‬ ‫ﺑﺴﺒﺐ‬ ‫ﺗﺰداد‬)‫ﺗﻨﺎﺳﺐ‬
‫طﺮدي‬(‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)∆V(
‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬:‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﻘﺼﺎن‬ ‫ﺑﺴﺒﺐ‬ ‫ﺗﻘﻞ‬
)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬)Q(
‫ﺻﻔﻴﺤﺘﻴﻬﺎ‬ ‫ﺑﲔ‬ ‫ﺍﻟﺒﻌﺪ‬ ‫ﻧﻘﺼﺎﻥ‬
1‫اﻟﺴﻌﺔ‬:‫ﻻن‬ ‫ﺗﺰداد‬
d
1
Cα‫اﻟﺴﻌﺔ‬:‫ﻻن‬ ‫ﺗﺰداد‬
d
1
Cα
2
‫اﻟﺸﺤﻨﺔ‬:‫ﺗﺰداد‬ ‫اﻟﺴﻌﺔ‬ ‫ﻻن‬ ‫ﺗﺰداد‬)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)∆V(
‫اﻟﺸﺤﻨﺔ‬:‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻻن‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﺗﺒﻘﻰ‬
3‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬:‫اﻟﻤﺼﺪر‬ ‫ﻟﻮﺟﻮد‬ ‫ﺛﺎﺑﺖ‬ ‫ﯾﺒﻘﻰ‬
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬:‫ﻻ‬ ‫ﯾﻘﻞ‬‫ﺗﺰداد‬ ‫اﻟﺴﻌﺔ‬ ‫ن‬)‫ﻋﻜﺴﻲ‬ ‫ﺗﻨﺎﺳﺐ‬(
‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬)Q(
4
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬:‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫ﻟﻨﻘﺼﺎن‬ ‫ﯾﺰداد‬
‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬)‫ﻋﻜﺴﻲ‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬
)∆V(
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬:‫ﯾﻘﻞ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻻن‬ ‫ﺛﺎﺑﺖ‬ ‫ﯾﺒﻘﻰ‬
‫وان‬ ‫ﯾﻘﻞ‬ ‫واﻟﺒﻌﺪ‬
d
V
E
∆
=
5
‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬:‫زﯾﺎد‬ ‫ﺑﺴﺒﺐ‬ ‫ﺗﺰداد‬‫اﻟﺸﺤﻨﺔ‬ ‫ة‬
)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)∆V(
‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬:‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﻘﺼﺎن‬ ‫ﺑﺴﺒﺐ‬ ‫ﺗﻘﻞ‬
)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬)Q(
‫ﻟﻠﺼﻔﻴﺤﺘﲔ‬ ‫ﺍﳌﺘﻘﺎﺑﻠﺔ‬ ‫ﺍﳌﺴﺎﺣﺔ‬ ‫ﺯﻳﺎﺩﺓ‬
1‫اﻟﺴﻌﺔ‬:‫ﻻن‬ ‫ﺗﺰداد‬ACα‫اﻟﺴﻌﺔ‬:‫ﻻن‬ ‫ﺗﺰداد‬ACα
2
‫اﻟﺸﺤﻨﺔ‬:‫ﺗﺰدا‬‫ﺗﺰداد‬ ‫اﻟﺴﻌﺔ‬ ‫ﻻن‬ ‫د‬)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)∆V(
‫اﻟﺸﺤﻨﺔ‬:‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻻن‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﺗﺒﻘﻰ‬
3‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬:‫اﻟﻤﺼﺪر‬ ‫ﻟﻮﺟﻮد‬ ‫ﺛﺎﺑﺖ‬ ‫ﯾﺒﻘﻰ‬
‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬:‫ﺗﺰداد‬ ‫اﻟﺴﻌﺔ‬ ‫ﻻن‬ ‫ﯾﻘﻞ‬)‫ﻋﻜﺴﻲ‬ ‫ﺗﻨﺎﺳﺐ‬(
‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬)Q(
4
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬:‫واﻟﺒﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻟﺜﺒﻮت‬ ‫ﺛﺎﺑﺖ‬
‫ﺑﯿﻦ‬‫ﺣﯿﺚ‬ ‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬:
d
V
E
∆
=
‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﻤﺠﺎل‬:‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﻘﺼﺎن‬ ‫ﺑﺴﺒﺐ‬ ‫ﯾﻘﻞ‬
)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺼﻔﯿﺤﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫ﺑﺜﺒﻮت‬)d(
5
‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬:‫اﻟﺸﺤﻨﺔ‬ ‫زﯾﺎدة‬ ‫ﺑﺴﺒﺐ‬ ‫ﺗﺰداد‬
)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﺜﺒﻮت‬)∆V(
‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬:‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﻘﺼﺎن‬ ‫ﺑﺴﺒﺐ‬ ‫ﺗﻘﻞ‬
)‫ﺗ‬‫طﺮدي‬ ‫ﻨﺎﺳﺐ‬(‫اﻟﺸﺤﻨﺔ‬ ‫ﺑﺜﺒﻮت‬)Q(

16. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-17-
‫ﺍﻟﻌﺎﺯﻝ‬ ‫ﺍﺩﺧﺎﻝ‬ ‫ﺑﻌﺪ‬ ‫ﺍﳊﻞ‬ ‫ﺧﻄﻮﺍﺕ‬
‫ﺍﻟﻔﺼﻞ‬ ‫ﲤﺎﺭﻳﻦ‬ ‫ﻣﻦ‬ ‫ﺍﻟﺜﺎﻧﻲ‬ ‫ﻭﺍﻟﺴﺆﺍﻝ‬ ‫ﺍﻷﻭﻝ‬ ‫ﺍﳌﺜﺎﻝ‬ ‫ﰲ‬ ‫ﻛﻤﺎ‬ ‫ﺍﻟﻮﺍﺣﺪﺓ‬ ‫ﻟﻠﻤﺘﺴﻌﺔ‬:
‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬ ‫ﻛﻮن‬ ‫ﻋﻠﻰ‬ ‫ﯾﻌﺘﻤﺪ‬ ‫واﻟﺤﻞ‬ ‫اﻟﻌﺎزل‬ ‫إدﺧﺎل‬ ‫ﺑﻌﺪ‬ ‫ﺑﺨﻄﻮﺗﯿﻦ‬ ‫ﯾﺤﻞ‬ ‫اﻟﻤﺴﺎﺋﻞ‬ ‫ﻣﻦ‬ ‫اﻟﻨﻮع‬ ‫ھﺬا‬)k(‫ﻣﺠﮭﻮل‬ ‫ام‬ ‫ﻣﻌﻠﻮم‬
‫اوﻻ‬:‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬ ‫ﯾﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬)k(‫ھﻲ‬ ‫اﻟﺤﻞ‬ ‫ﺧﻄﻮات‬ ‫ﻓﺎن‬ ‫ﻣﻌﻠﻮم‬:
1- CK =KC
2-
K
K
K
V
Q
C
∆
=
♦‫اﻟﻌﺎزﻟﺔ‬ ‫اﻟﻤﺎدة‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬ ‫اﺳﺘﺨﺮاج‬ ‫اﻷوﻟﻰ‬ ‫ﻟﻠﺨﻄﻮة‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬.
♦‫ﻮد‬‫ﺑﻮﺟ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫او‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﺸﺤﻨﺔ‬ ‫اﻣﺎ‬ ‫اﺳﺘﺨﺮاج‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫ﻟﻠﺨﻄﻮة‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﻮن‬‫ﻛ‬ ‫ﺎة‬‫ﻣﺮاﻋ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎزل‬‫اﻟﻌ‬
‫ام‬ ‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬‫ﻋﻨﮫ‬ ‫ﻣﻨﻔﺼﻠﺔ‬.
‫ﺎزل‬‫اﻟﻌ‬ ‫ﻞ‬‫ﻗﺒ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻧﻔﺴﮫ‬ ‫ھﻮ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻓﺎن‬ ‫ﺑﺎﻟﺒﻄﺎرﯾﺔ‬ ‫ﻣﺘﺼﻠﺔ‬ ‫زاﻟﺖ‬ ‫ﻣﺎ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻓﻌﻨﺪﻣﺎ‬
)‫ﺛﺎﺑﺖ‬(‫اﻟﻌﺎزل‬ ‫ﻗﺒﻞ‬ ‫اﻟﺠﮭﺪ‬ ‫وﻓﺮق‬ ‫اﻻوﻟﻰ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫اﻟﺴﻌﺔ‬ ‫ﺑﻤﻌﺮﻓﺔ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺴﺘﺨﺮج‬ ‫ان‬ ‫اﻻ‬ ‫ﻋﻠﯿﻚ‬ ‫ﻓﻤﺎ‬.
‫وادﺧﻞ‬ ‫اﻟﺒﻄﺎرﯾﺔ‬ ‫ﻋﻦ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻓﺼﻞ‬ ‫وﻋﻨﺪ‬‫ﺤﻨﺘﮭﺎ‬‫ﺷ‬ ‫ﺖ‬‫ﺗﺜﺒ‬ ‫ﻔﯿﺤﺘﮭﺎ‬‫ﺻ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫اﻟﻌﺎزل‬)‫ﻞ‬‫ﻗﺒ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﺴﺎوي‬‫ﺗ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﺪ‬‫ﺑﻌ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬
‫اﻟﻌﺎزل‬(‫ﻞ‬‫ﻗﺒ‬ ‫ﺸﺤﻨﺔ‬‫واﻟ‬ ‫ﻰ‬‫اﻻوﻟ‬ ‫ﺔ‬‫اﻟﻨﻘﻄ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺴﻌﺔ‬‫اﻟﻤﺘ‬ ‫ﺳﻌﺔ‬ ‫ﺑﻤﻌﺮﻓﺔ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺟﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺗﺴﺘﺨﺮج‬ ‫ان‬ ‫اﻻ‬ ‫ﻋﻠﯿﻚ‬ ‫وﻣﺎ‬
‫اﻟﻌﺎزل‬.
‫ﺛﺎﻧﯿﺎ‬:‫اﻟﻌﺰل‬ ‫ﺛﺎﺑﺖ‬ ‫ﯾﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬K‫اﻟﻤﺠﮭﻮل‬ ‫ھﻮ‬:
‫اﻟﺨﻄﻮ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫اﻟﺨﻄﻮة‬ ‫ﻧﻘﺪم‬‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺎزل‬‫اﻟﻌ‬ ‫ﻮد‬‫ﺑﻮﺟ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻗﺴﻤﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻮﺟﻮد‬ ‫اﻟﺴﻌﺔ‬ ‫ﻹﯾﺠﺎد‬ ‫اﻷوﻟﻰ‬ ‫ط‬
‫ﺔ‬ ‫ﺑﺎﻟﺒﻄﺎرﯾ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﻞ‬‫ھ‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﺔ‬ ‫ﻣﻌﺮﻓ‬ ‫ﺪ‬ ‫ﺑﻌ‬ ‫ﺎزل‬ ‫اﻟﻌ‬ ‫ﻮد‬ ‫ﺑﻮﺟ‬)‫ﺔ‬ ‫اﻟﺤﺎﻟ‬ ‫ﺬه‬ ‫ھ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺪھﺎ‬ ‫ﺟﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺖ‬‫ﯾﺜﺒ‬ ‫ﺚ‬‫ﺣﯿ‬(‫ﻦ‬ ‫ﻋ‬ ‫ﺼﻠﺔ‬ ‫ﻣﻨﻔ‬ ‫ام‬
‫اﻟﺒﻄﺎرﯾﺔ‬)‫اﻟﺤﺎﻟﺔ‬ ‫ھﺬه‬ ‫ﻓﻲ‬ ‫ﺷﺤﻨﺘﮭﺎ‬ ‫ﺗﺜﺒﺖ‬ ‫ﺣﯿﺚ‬.(
‫ﺗﻮﺍﱄ‬ ‫ﺃﻭ‬ ‫ﺗﻮﺍﺯﻱ‬ ‫ﻣﺮﺑﻮﻃﺔ‬ ‫ﺍﳌﺘﺴﻌﺎﺕ‬ ‫ﻣﻦ‬ ‫ﻤﻮﻉ‬‫ﻭﺍﳋﺎﻣﺲ‬ ‫ﻭﺍﻟﺮﺍﺑﻊ‬ ‫ﺍﻟﺜﺎﻟﺚ‬ ‫ﺍﻟﺴﺆﺍﻝ‬ ‫ﰲ‬ ‫ﻛﻤﺎ‬
‫ﻓﺮﻋﯿﺔ‬ ‫ﺧﻄﻮات‬ ‫ھﻲ‬ ‫واﻟﺒﻘﯿﺔ‬ ‫أﺳﺎﺳﯿﺔ‬ ‫ﺧﻄﻮات‬ ‫ﺛﻼث‬ ‫ﻋﻠﻰ‬ ‫ﻣﻌﺘﻤﺪا‬ ‫اﻟﺤﻞ‬ ‫ﯾﻜﻮن‬:
‫ﻋﻠﻰ‬ ‫ﻣﻌﺘﻤﺪة‬ ‫اﻷﺳﺎﺳﯿﺔ‬ ‫ﻓﺎﻟﺨﻄﻮات‬K‫ﻣﺠﮭﻮل‬ ‫ام‬ ‫ﻣﻌﻠﻮم‬
‫اوﻻ‬:‫ﯾﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬K‫اﻵﺗﯿﺔ‬ ‫اﻟﺨﻄﻮات‬ ‫ﻧﺘﺒﻊ‬ ‫ﻣﺜﻼ‬ ‫اﻷوﻟﻰ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﺎزل‬ ‫وادﺧﻞ‬ ‫ﻣﻌﻠﻮم‬:
1-‫ﻧﺠﺪ‬C1K‫اﻟﻌ‬ ‫ﻣﻦ‬‫ﻼﻗﺔ‬:C1K=KC1
2-‫ﺪ‬‫ﻧﺠ‬C(eq)k‫ﺴﻌﺎت‬‫اﻟ‬ ‫ﻮع‬ ‫ﻣﺠﻤ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﺎ‬ ‫اﻣ‬ ‫ﺮﺑﻂ‬‫اﻟ‬ ‫ﻮاص‬ ‫ﺧ‬ ‫ﻦ‬ ‫ﻣ‬)‫ﻮازي‬ ‫ﺗ‬ ‫ﺮﺑﻂ‬‫اﻟ‬ ‫ﺎن‬ ‫ﻛ‬ ‫اذا‬(‫ﺴﻌﺎت‬ ‫اﻟ‬ ‫ﻮع‬ ‫ﻣﺠﻤ‬ ‫ﻮب‬ ‫ﻣﻘﻠ‬ ‫ﻦ‬‫ﻣ‬ ‫او‬
)‫ﺗﻮاﻟﻲ‬ ‫اﻟﺮﺑﻂ‬ ‫ﻛﺎن‬ ‫اذا‬(
3-‫ﺎﻧﻮن‬ ‫اﻟﻘ‬ ‫ﺴﺘﺨﺪم‬ ‫ﻧ‬)
k)t(
k)t(
eqk
V
Q
C
∆
=(‫ﺎد‬ ‫ﻹﯾﺠ‬ ‫ﺎ‬ ‫أﻣ‬)QTK(‫ﺎد‬ ‫ﻹﯾﺠ‬ ‫أو‬)∆VTk(‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﺔ‬ ‫اﻟﻤﺠﻤﻮﻋ‬ ‫ﻞ‬ ‫ھ‬ ‫ﺔ‬ ‫ﻣﻌﺮﻓ‬ ‫ﺪ‬ ‫ﺑﻌ‬
‫ﺑﺎﻟﺒﻄﺎرﯾﺔ‬)‫ﺖ‬‫ﺛﺎﺑ‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺒﻘﻰ‬ ‫ﺣﯿﺚ‬(‫ﺎ‬‫ﻋﻨﮭ‬ ‫ﺼﻠﺔ‬‫ﻣﻨﻔ‬ ‫ام‬)‫ﺔ‬‫ﺛﺎﺑﺘ‬ ‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬ ‫ﻰ‬‫ﺗﺒﻘ‬ ‫ﺚ‬‫ﺣﯿ‬.(‫ﻰ‬‫ﻋﻠ‬ ‫ﺪ‬‫ﻧﻌﺘﻤ‬ ‫ﻚ‬‫ذﻟ‬ ‫ﺪ‬‫ﺑﻌ‬
‫ﻂ‬‫رﺑ‬ ‫ﻲ‬‫وﻓ‬ ‫ﺴﻌﺔ‬‫ﻣﺘ‬ ‫ﻞ‬‫ﻛ‬ ‫ﺪ‬‫ﺟﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺴﺎوي‬‫ﯾ‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫اﻟﺘﻮازي‬ ‫رﺑﻂ‬ ‫ﻓﻔﻲ‬ ‫ﺗﻮاﻟﻲ‬ ‫أم‬ ‫ﺗﻮازي‬ ‫اﻟﺮﺑﻂ‬ ‫ﺧﻮاص‬
‫ﻣﺘﺴﻌﺔ‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻌﺎزل‬ ‫ﺑﻌﺪ‬ ‫ﻛﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫اﻟﺘﻮاﻟﻲ‬.
‫ﺛﺎﻧﯿﺎ‬:‫ﯾﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬K‫ﻧﺘﺒﻊ‬ ‫ﻣﺜﻼ‬ ‫اﻷوﻟﻰ‬ ‫ﺻﻔﯿﺤﺘﻲ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﺰل‬ ‫وادﺧﻞ‬ ‫ﻣﺠﮭﻮل‬‫ﻧﻔﺲ‬‫اﻟﺨﻄﻮة‬ ‫ﻧﺠﻌﻞ‬ ‫وﻟﻜﻦ‬ ‫اﻟﺨﻄﻮات‬‫ﻰ‬‫اﻻوﻟ‬
‫اﻻوﻟﻰ‬ ‫ھﻲ‬ ‫اﻟﺜﺎﻟﺜﺔ‬ ‫واﻟﺨﻄﻮة‬ ‫اﻟﺜﺎﻟﺜﺔ‬ ‫ھﻲ‬‫ﯾﺎﺗﻲ‬ ‫وﻛﻤﺎ‬:
1-‫ﺎﻧﻮن‬ ‫اﻟﻘ‬ ‫ﺴﺘﺨﺪم‬ ‫ﻧ‬)
k)t(
k)t(
eqk
V
Q
C
∆
=(‫ﺎد‬ ‫ﻻﯾﺠ‬C(eq)k‫ﺔ‬ ‫ﺑﺎﻟﺒﻄﺎرﯾ‬ ‫ﺼﻠﺔ‬ ‫ﻣﺘ‬ ‫ﺔ‬ ‫اﻟﻤﺠﻤﻮﻋ‬ ‫ﻞ‬ ‫ھ‬ ‫ﺔ‬ ‫ﻣﻌﺮﻓ‬ ‫ﺪ‬ ‫ﺑﻌ‬
)‫ﺛﺎﺑﺖ‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﯾﺒﻘﻰ‬ ‫ﺣﯿﺚ‬(‫ﻋﻨﮭﺎ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫ام‬)‫ﺛﺎﺑﺘﺔ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﺒﻘﻰ‬ ‫ﺣﯿﺚ‬. (
2-‫ﺗﻮازي‬ ‫اﻟﺮﺑﻂ‬ ‫ﺧﻮاص‬ ‫ﻧﺴﺘﺨﺪم‬)‫ﺴﻌﺎت‬‫اﻟ‬ ‫ﻣﺠﻤﻮع‬(‫ﻮاﻟﻲ‬‫اﻟﺘ‬ ‫او‬)‫ﺴﻌﺎت‬‫اﻟ‬ ‫ﻮب‬‫ﻣﻘﻠ‬(‫ﻞ‬‫ادﺧ‬ ‫ﻲ‬‫واﻟﺘ‬ ‫ﺔ‬‫اﻟﻤﺠﮭﻮﻟ‬ ‫ﺴﻌﺔ‬‫اﻟ‬ ‫ﺎد‬‫ﻻﯾﺠ‬
‫اﻟﻌﺎزل‬ ‫ﻋﻠﯿﮭﺎ‬.
3-‫ﻧﺠﺪ‬K‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬:CK =KC.

17. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-18-
‫اﻻول‬ ‫اﻟﻔﺼﻞ‬ ‫ﻗﻮاﻧﻴﻦ‬
‫اوﻻ‬:‫واﺣﺪة‬ ‫ﻣﺘﺴﻌﺔ‬
♦‫ﻫﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫اﻟﻌﺎزل‬ ‫ﻛﺎن‬ ‫اذا‬)‫اﻟﻌﺎزل‬ ‫ادﺧﺎل‬ ‫ﻗﺒﻞ‬(:
,
♦‫اﻟﻬﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫ﻏﻴﺮ‬ ‫اﻟﻌﺎزل‬ ‫ﻛﺎن‬ ‫اذا‬)‫اﻟﻌﺎزل‬ ‫ادﺧﺎل‬ ‫ﺑﻌﺪ‬(:
1(‫اﻟﻘﻮاﻧﻴﻦ‬:
,
2(‫اﻟﻌﻼﻗﺎت‬:
‫ﺑﺎﻟﻤﺼﺪر‬ ‫ﻣﺘﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬‫اﻟﻤﺼﺪر‬ ‫ﻋﻦ‬ ‫ﻣﻨﻔﺼﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
CkCk =CkCk =
QkQk =QQk =
VVk ∆=∆
k
V
Vk
∆
=∆
EEk =
k
E
Ek =
PEkPEk =
k
PE
PEk =
‫ﻣﺘﻮاﻟﻴﺔ‬ ‫او‬ ‫ﻣﺘﻮازﻳﺔ‬ ‫ﻣﺘﺴﻌﺎت‬ ‫ﻣﺠﻤﻮﻋﺔ‬‫وﻣﺘﻮاﻟﻴﺔ‬ ‫ﻣﺘﻮازﻳﺔ‬ ‫او‬)‫ﻣﺨﺘﻠﻂ‬(:
‫اوﻻ‬:‫اﻟﻘﻮاﻧﻴﻦ‬:
‫ﻛﺎن‬ ‫اذا‬‫ﻫﻮاء‬ ‫او‬ ‫ﻓﺮاغ‬ ‫اﻟﻌﺎزل‬)‫اﻟﻌﺎزل‬ ‫ادﺧﺎل‬ ‫ﻗﺒﻞ‬(:
eq
2
T
T
2
TeqTTTT
C
Q
.
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE =∆=∆=
T
T
eq
V
Q
C
∆
=
k
2
k
k
2
kkkkkk
C
Q
.
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE =∆=∆=
d
V
E k
k
∆
=d
A
kCor
V
Q
C k
k
k
k οε=
∆
=
C
Q
.
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE
2
2
=∆=∆=
d
V
E
∆
=
d
A
Cor
V
Q
C οε=
∆
=

18. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-19-
‫اﻟﻬﻮاء‬ ‫او‬ ‫اﻟﻔﺮاغ‬ ‫ﻏﻴﺮ‬ ‫اﻟﻌﺎزل‬ ‫ﻛﺎن‬ ‫اذا‬)‫اﻟﻌﺎزل‬ ‫ادﺧﺎل‬ ‫ﺑﻌﺪ‬(:
‫ﺛﺎﻧﻴﺎ‬:‫اﻟﺨﻮاص‬
‫ت‬‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫رﺑﻂ‬‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫رﺑﻂ‬
1
‫ﻌﺎت‬ ‫ﺳ‬ ‫ﻮع‬ ‫ﻣﺠﻤ‬ ‫ﺴﺎوي‬ ‫ﺗ‬ ‫ﺔ‬ ‫ﻟﻠﻤﺠﻤﻮﻋ‬ ‫ﺔ‬ ‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬ ‫اﻟ‬
‫ان‬ ‫أي‬ ‫اﻟﻤﺘﺴﻌﺎت‬:
Ceq=C1 + C2 + C3 + ……. Cn
‫ﻮع‬ ‫ﻣﺠﻤ‬ ‫ﺴﺎوي‬ ‫ﯾ‬ ‫ﺔ‬ ‫ﻟﻠﻤﺠﻤﻮﻋ‬ ‫ﺔ‬ ‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬ ‫اﻟ‬ ‫ﻮب‬ ‫ﻣﻘﻠ‬
‫ان‬ ‫أي‬ ‫اﻟﺴﻌﺎت‬ ‫ﻣﻘﻠﻮب‬:
n321eq
C
1
.......
C
1
C
1
C
1
C
1
+++=
2
‫اﻟ‬‫ان‬ ‫أي‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﺷﺤﻨﺎت‬ ‫ﻣﺠﻤﻮع‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻜﻠﯿﺔ‬ ‫ﺸﺤﻨﺔ‬:
QT =Q1 + Q2 + Q3 + …….Qn
‫ﺴﻌﺎت‬‫اﻟﻤﺘ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺴﻌﺔ‬‫ﻣﺘ‬ ‫أي‬ ‫ﺤﻨﺔ‬‫ﺷ‬ ‫ﺴﺎوي‬‫ﺗ‬ ‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺸﺤﻨﺔ‬‫اﻟ‬
)‫ﺛﺎﺑﺘﺔ‬ ‫اﻟﺸﺤﻨﺔ‬(‫ان‬ ‫أي‬:
QT =Q1 = Q2 = Q3 = …….Qn
3
‫ﻦ‬ ‫ﻣ‬ ‫ﺴﻌﺔ‬ ‫ﻣﺘ‬ ‫أي‬ ‫ﺪ‬ ‫ﺟﮭ‬ ‫ﺮق‬ ‫ﻓ‬ ‫ﺴﺎوي‬ ‫ﯾ‬ ‫ﻲ‬ ‫اﻟﻜﻠ‬ ‫ﺪ‬ ‫اﻟﺠﮭ‬ ‫ﺮق‬ ‫ﻓ‬
‫اﻟﻤﺘﺴﻌﺎت‬)‫ﺛﺎﺑﺖ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬(‫ان‬ ‫أي‬:
∆VT =∆V1 = ∆V2 =∆V3 =…….∆Vn
‫ﻟﻠﻤﺘﺴﻌﺎت‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻣﺠﻤﻮع‬ ‫ﯾﺴﺎوي‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬
‫ان‬ ‫أي‬:
∆VT =∆V1 + ∆V2 + ∆V3 + ……. ∆Vn
4.........PEPEPEPE 321T +++=..........PEPEPEPE 321T +++=
5
‫اﻟﺴﻌﺔ‬ ‫اﻟﻤﺘﻤﺎﺛﻠﺔ‬ ‫اﻟﻤﺘﺴﻌﺎت‬ ‫ﻣﻦ‬ ‫ﻋﺪد‬ ‫ﻻي‬)‫اﻟﻤﺘﺴﺎوﯾﺔ‬(‫ﻓﺎن‬:
‫ﺔ‬ ‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﻌﺔ‬ ‫ﺳ‬=‫ﺪد‬ ‫ﻋ‬‫ﺴﻌﺎت‬ ‫اﻟﻤﺘ‬×‫أي‬ ‫ﻌﺔ‬ ‫ﺳ‬
‫ﻣﺘﺴﻌﺘﺔ‬
nCCeq =
‫ﺴﻌﺔ‬ ‫اﻟ‬ ‫ﺔ‬ ‫اﻟﻤﺘﻤﺎﺛﻠ‬ ‫ﺴﻌﺎت‬ ‫اﻟﻤﺘ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﺪد‬ ‫ﻋ‬ ‫ﻻي‬)‫ﺴﺎوﯾﺔ‬ ‫اﻟﻤﺘ‬(
‫ﻓﺎن‬:
‫ﺔ‬ ‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﻌﺔ‬ ‫ﺳ‬=‫ﺴﻌﺔ‬ ‫ﻣﺘ‬ ‫أي‬ ‫ﻌﺔ‬ ‫ﺳ‬/‫ﺪد‬ ‫ﻋ‬
‫اﻟﻤﺘﺴﻌﺎت‬
n
C
Ceq =
eqk
2
Tk
Tk
2
TkeqkTkTkTkTk
C
Q
.
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE =∆=∆=
Tk
Tk
eqk
V
Q
C
∆
=
QTK = QT ‫ﻟﻠﻤﻨﻔﺼﻠﺔ‬ or ∆VTk = ∆VT ‫ﻟﻠﻤﺘﺼﻠﺔ‬ , Ck=k C
C1
C2
C3
∆VT
∆VT
C1 C2 C3

19. ‫اﻷول‬ ‫اﻟﻔﺼﻞ‬:‫اﻟﻤﺘﺴﻌ‬‫ﺎت‬Capacitors‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-20-
‫اﻟﻤﺘﺴﻌﺔ‬ ‫وﺗﻔﺮﻳﻎ‬ ‫ﺷﺤﻦ‬:
‫اوﻻ‬:‫اﻟﻤﻔﺘﺎح‬ ‫ﻏﻠﻖ‬ ‫ﻟﺤﻈﺔ‬
0PE,0E,0V,0Q
R
V
I,VV
C
battery
batteryR
===∆=
∆
=∆=∆
‫ﺛﺎﻧﻴﺎ‬:‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺷﺤﻦ‬ ‫اﺗﻤﺎم‬ ‫ﺑﻌﺪ‬:
C
Q
2
1
PEor)V.(C
2
1
PEorQ.V
2
1
PE
,
d
V
E,V.CQ,VV
0I,0V
2
2
C
C
CbatteryC
R
=∆=∆=
∆
=∆=∆=∆
==∆
‫ﺛﺎﻧﻴﺎ‬:‫اﻵﺗﻴﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬ ‫ﻳﺤﺴﺐ‬ ‫اﻟﺘﻔﺮﻳﻎ‬ ‫ﺗﻴﺎر‬:
R
V
I C∆
=

20. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-21-
×
‫اﻟﻤﻐﻨﺎﻃﻴﺴﻴﺔ‬ ‫واﻟﻘﻮة‬ ‫اﻟﻜﻬﺮﺑﺎﺋﻴﺔ‬ ‫اﻟﻘﻮة‬:
‫ﻣﺸﺤﻮن‬ ‫ﺟﺴﻴﻢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺆﺛﺮة‬ ‫اﻟﻜﻬﺮﺑﺎﺋﻴﺔ‬ ‫اﻟﻘﻮة‬ ‫ﻋﻦ‬ ‫ﻳﻌﺒﺮ‬‫وﻋﻦ‬ ‫ﻛﻬﺮﺑﺎﺋﻲ‬ ‫ﻣﺠﺎل‬ ‫داﺧﻞ‬ ‫ﻳﺘﺤﺮك‬‫اﻟﻤـﺆﺛﺮة‬ ‫اﻟﻤﻐﻨﺎﻃﻴـﺴﻴﺔ‬ ‫واﻟﻘﻮة‬
‫ﻣﺸﺤﻮن‬ ‫ﺟﺴﻴﻢ‬ ‫ﻋﻠﻰ‬‫ﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﻣﺠﺎل‬ ‫داﺧﻞ‬ ‫ﻳﺘﺤﺮك‬‫اﻻﺗﻴﺔ‬ ‫اﻟﺮﻳﺎﺿﻴﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺎت‬:
‫اﻟﻜﮭﺮﺑ‬ ‫اﻟﻘﻮة‬ ‫وﺣﺪة‬‫ﺎﺋﯿﺔ‬)FE(‫اﻟﻨﯿﻮﺗﻦ‬ ‫ھﻲ‬)N(‫ﺑﺎﻟﻜﻮﻟﻮم‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬)C(‫ﺑﻮﺣﺪة‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫واﻟﻤﺠﺎل‬)N/C.(
‫اﻵﺗﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫ﻓﯿﻌﻄﻰ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬ ‫اﻟﻘﻮة‬ ‫ﻣﻘﺪار‬ ‫اﻣﺎ‬:
‫ﺣﯿﺚ‬:
FB:‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬ ‫اﻟﻘﻮة‬)N(‫ﺣﯿﺚ‬)
→→→
ν⊥ B,FB(،q:‫ﺷﺤﻨﺔ‬‫ﻛﻮﻟﻮم‬ ‫ﺑﻮﺣﺪة‬ ‫اﻟﺠﺴﯿﻢ‬)C(
ν:‫ﺑﻮﺣﺪة‬ ‫اﻟﺠﺴﯿﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻣﻘﺪار‬)m/sec(.
B:‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻛﺜﺎﻓﺔ‬)‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﺷﺪة‬ ‫او‬(‫ﺗﺴﻼ‬ ‫ﺑﻮﺣﺪة‬)T(‫ﺣﯿﺚ‬)T=wb/m2
(‫ﺮى‬‫اﺧ‬ ‫ﺪة‬‫وﺣ‬ ‫وھﻨﺎﻟﻚ‬
‫اﻟﻜﺎوس‬ ‫وھﻲ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻛﺜﺎﻓﺔ‬ ‫ﻟﻘﯿﺎس‬َ)gauss(‫ورﻣﺰه‬)G(‫وان‬)G=10-4
T(
‫ﻟﻠﺘﺤﻮﯾﻞ‬ ‫ﻟﺬﻟﻚ‬‫ﻣﻦ‬:
θ:‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﺘﺠﮫ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺤﺼﻮرة‬ ‫اﻟﺰاوﯾﺔ‬)
→
ν(‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻛﺜﺎﻓﺔ‬ ‫وﻣﺘﺠﮫ‬)
→
B. (
‫ﻣﻼﺣﻈ‬‫ﺎت‬/
1-‫ﻋﻨﺪﻣﺎ‬)
→→
⊥ν B(‫ﻓﺎن‬)θ=90ͦ(‫وان‬)sin90ͦ=1(‫ﯾﺘﺎﺛ‬ ‫ﻟﺬﻟﻚ‬‫اﻟ‬ ‫ﺮ‬‫ﺴﻲ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫داﺧﻞ‬ ‫واﻟﻤﺘﺤﺮك‬ ‫اﻟﻤﺸﺤﻮن‬ ‫ﺠﺴﯿﻢ‬
‫ﻣﻐﻨﺎطﯿﺴﯿﺔ‬ ‫ﻗﻮة‬ ‫ﺑﺎﻋﻈﻢ‬.
2-‫ﻋﻨﺪﻣﺎ‬‫ﺗﻜﻮن‬)
→
B/ /
→
ν(‫ﻓﺎن‬)θ=0(‫وان‬)sin0=0(‫اﻟﺠﺴ‬ ‫ﯾﺘﺎﺛﺮ‬ ‫ﻻ‬ ‫ﻟﺬﻟﻚ‬‫ﯿ‬‫اﻟﺤﺎﻟﺔ‬ ‫ھﺬه‬ ‫ﻓﻲ‬ ‫ﻣﻐﻨﺎطﯿﺴﯿﺔ‬ ‫ﻗﻮة‬ ‫ﺑﺎﯾﺔ‬ ‫ﻢ‬.
‫ﻣﻼﺣﻈ‬‫ﺎت‬/
1-‫ان‬‫ﻓﻲ‬ ‫اﻟﻤﺆﺛﺮة‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬ ‫اﻟﻘﻮة‬‫ﺎه‬‫ﻻﺗﺠ‬ ‫ﺎﻛﺲ‬‫ﻣﻌ‬ ‫ﺎه‬‫ﺑﺎﺗﺠ‬ ‫ﻮن‬‫ﺗﻜ‬ ‫ﺴﻲ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺘﺤﺮﻛﺔ‬ ‫اﻟﺴﺎﻟﺒﺔ‬ ‫اﻟﺸﺤﻨﺔ‬
‫اﻟﻤﻐﻨﺎ‬ ‫اﻟﻘﻮة‬‫اﻟﻤﻮﺟﺒﺔ‬ ‫اﻟﺸﺤﻨﺔ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺆﺛﺮة‬ ‫طﯿﺴﯿﺔ‬.
2-‫ﺰ‬ ‫اﻟﺮﻣ‬ ‫ﺴﺘﺨﺪم‬ ‫ﯾ‬‫ﻞ‬ ‫ﻣﺜ‬ ‫ﺔ‬ ‫اﻟﻔﯿﺰﯾﺎﺋﯿ‬ ‫ﺔ‬ ‫اﻟﻜﻤﯿ‬ ‫ان‬ ‫ﻰ‬ ‫ﻋﻠ‬ ‫ﺔ‬ ‫ﻟﻠﺪﻻﻟ‬)......F,,B
→→→
ν(‫ﺪاﺧﻞ‬ ‫اﻟ‬ ‫ﻮ‬ ‫ﻧﺤ‬ ‫ﮫ‬ ‫ﻣﺘﺠ‬
)‫اﻟﻨﺎظﺮ‬ ‫ﻋﻦ‬ ‫ﺑﻌﯿﺪا‬(
3-‫اﻟﺮﻣﺰ‬ ‫ﯾﺴﺘﺨﺪم‬‫ﻣﺜﻞ‬ ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺔ‬ ‫ان‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺪﻻﻟﺔ‬)......F,,B
→→→
ν(‫اﻟﺨﺎرج‬ ‫ﻧﺤﻮ‬ ‫ﻣﺘﺠﮫ‬)‫اﻟﻨﺎظﺮ‬ ‫ﺑﺎﺗﺠﺎه‬(
4-‫ﺎﻟﻘﻮة‬ ‫ﺑ‬ ‫ﺎﺛﺮ‬ ‫ﯾﺘ‬ ‫ﻻ‬ ‫ﺎ‬ ‫ﺑﯿﻨﻤ‬ ‫ﺎ‬ ‫ﻣﺘﺤﺮﻛ‬ ‫او‬ ‫ﺎﻛﻨﺎ‬ ‫ﺳ‬ ‫ﮫ‬ ‫ﻛﻮﻧ‬ ‫ﻦ‬ ‫ﻋ‬ ‫ﺮ‬ ‫اﻟﻨﻈ‬ ‫ﺾ‬ ‫ﺑﻐ‬ ‫ﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿ‬ ‫ﺎﻟﻘﻮة‬ ‫ﺑ‬ ‫ﺎﺛﺮ‬ ‫ﯾﺘ‬ ‫ﺸﺤﻮن‬ ‫اﻟﻤ‬ ‫ﺴﯿﻢ‬ ‫اﻟﺠ‬ ‫ان‬
‫اﻻ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬‫ﻣﺘﺤﺮﻛﺎ‬ ‫ﻛﺎن‬ ‫اذا‬
θν= BSinqFB
EqFE =
)10( 4−
×
)10( 4
×
G T

21. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-22-
5-‫ﺎﺋﻲ‬ ‫اﻟﻜﮭﺮﺑ‬ ‫ﺎل‬ ‫اﻟﻤﺠ‬ ‫ﺎه‬ ‫اﺗﺠ‬ ‫ان‬)
→
E(‫ﺴﺎﻟﺒﺔ‬ ‫اﻟ‬ ‫ﺸﺤﻨﺔ‬ ‫اﻟ‬ ‫ﺎه‬ ‫ﺑﺎﺗﺠ‬ ‫ﺔ‬ ‫اﻟﻤﻮﺟﺒ‬ ‫ﺸﺤﻨﺔ‬ ‫اﻟ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﻮن‬ ‫ﯾﻜ‬‫ﺎل‬ ‫اﻟﻤﺠ‬ ‫ﻮط‬ ‫ﺧﻄ‬ ‫ﺎ‬ ‫ﺑﯿﻨﻤ‬
‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬)
→
B(‫اﻟﺸﻤﺎﻟﻲ‬ ‫اﻟﻘﻄﺐ‬ ‫ﻣﻦ‬ ‫ﺗﺘﺠﮫ‬)N(‫ﻮﺑﻲ‬‫اﻟﺠﻨ‬ ‫ﺐ‬‫اﻟﻘﻄ‬ ‫اﻟﻰ‬)S(‫ﺎ‬‫دورﺗﮭ‬ ‫ﻞ‬‫ﺗﻜﻤ‬ ‫ﻢ‬‫ﺛ‬ ‫ﺎطﯿﺲ‬‫اﻟﻤﻐﻨ‬ ‫ﺎرج‬‫ﺧ‬‫ﻞ‬‫داﺧ‬
‫اﻟﻤﻐﻨﺎطﯿﺲ‬‫اﻟﺸﻤﺎﻟﻲ‬ ‫اﻟﻘﻄﺐ‬ ‫اﻟﻰ‬ ‫اﻟﺠﻨﻮﺑﻲ‬ ‫اﻟﻘﻄﺐ‬ ‫ﻣﻦ‬.
‫اﻟﺤﺮﻛﻴﺔ‬ ‫اﻟﻜﻬﺮﺑﺎﺋﻴﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫اﻟﻘﻮة‬)εmotional(:
‫اﻟﺬي‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﺑﮭﺎ‬ ‫وﯾﻘﺼﺪ‬‫ﯾﺘﻮﻟﺪ‬)‫ﯾ‬ُ‫ﺴﺘﺤﺚ‬(‫ﺎل‬‫ﻣﺠ‬ ‫ﻞ‬‫داﺧ‬ ‫ﺴﺎق‬‫اﻟ‬ ‫ﺬه‬‫ھ‬ ‫ﺔ‬‫ﻟﺤﺮﻛ‬ ‫ﺔ‬‫ﻧﺘﯿﺠ‬ ‫ﻠﺔ‬‫ﻣﻮﺻ‬ ‫ﺳﺎق‬ ‫طﺮﻓﻲ‬ ‫ﻋﻠﻰ‬
‫اﻟﻜﮭﺮوﻣﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﺤﺚ‬ ‫ﺣﺎﻻت‬ ‫ﻣﻦ‬ ‫ﺧﺎﺻﺔ‬ ‫ﺣﺎﻟﺔ‬ ‫وﺗﻌﺪ‬ ‫ﻣﻨﺘﻈﻢ‬ ‫ﻣﻐﻨﺎطﯿﺴﻲ‬.
♦‫ﻓ‬‫ﺎ‬‫طﻮﻟﮭ‬ ‫ﻠﺔ‬‫ﻣﻮﺻ‬ ‫ﺎق‬‫ﺳ‬ ‫ﺮك‬‫ﺗﺘﺤ‬ ‫ﺪﻣﺎ‬‫ﻌﻨ‬)l(‫ﺪة‬‫ﺑﻮﺣ‬)m(‫ﺴﺮﻋﺔ‬‫ﺑ‬)ν(‫ﺪة‬‫ﺑﻮﺣ‬)m/sec(‫ﺘﻈﻢ‬‫ﻣﻨ‬ ‫ﺴﻲ‬‫ﻣﻐﻨﺎطﯿ‬ ‫ﺎل‬‫ﻣﺠ‬ ‫ﻲ‬‫ﻓ‬
‫ﻓﯿﻀﮫ‬ ‫ﻛﺜﺎﻓﺔ‬)B(‫ﺗﺴﻼ‬ ‫ﺑﻮﺣﺪة‬)T(‫ﻣﺘﺠﮫ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺰاوﯾﺔ‬ ‫ﺗﻜﻮن‬ ‫ﺑﺤﯿﺚ‬)
→
ν(‫وﻣﺘﺠﮫ‬)
→
B(‫ﺗﺴﺎوي‬)θ(‫ﻋﻠﻰ‬ ‫ﺗﺘﻮﻟﺪ‬ ‫ﻓﺴﻮف‬
‫ﻛﮭﺮﺑﺎﺋﯿﺔ‬ ‫داﻓﻌﺔ‬ ‫ﻗﻮة‬ ‫اﻟﺴﺎق‬ ‫طﺮﻓﻲ‬‫ﻣﺤﺘﺜﺔ‬‫ﺣﺮﻛﯿﺔ‬)εmotional(‫اﻟﺘﺎﻟﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬ ‫ﺗﻌﻄﻰ‬:
•‫ﻋﻨﺪﻣﺎ‬)
→→
⊥ν B(‫ﻓﺎن‬)°=θ 90(‫وان‬)190sin =°(‫اﻋ‬ ‫ﺗﺘﻮﻟﺪ‬ ‫ﻟﺬﻟﻚ‬‫ﺣﺮﻛﯿﺔ‬ ‫ﻣﺤﺘﺜﺔ‬ ‫ﻛﮭﺮﺑﺎﺋﯿﺔ‬ ‫داﻓﻌﺔ‬ ‫ﻗﻮة‬ ‫ﻈﻢ‬.
•‫ﻋﻨﺪﻣﺎ‬)
→
B/ /
→
ν(‫ﻓﺎن‬)θ=0(‫وان‬)sin0=0(‫ﺗﺘﻮﻟﺪ‬ ‫ﻻ‬ ‫ﻟﺬﻟﻚ‬)εmotional(‫اﻟﺴﺎق‬ ‫طﺮﻓﻲ‬ ‫ﻋﻠﻰ‬.
•‫ﺪاﺋﺮة‬ ‫ﻟﻠ‬ ‫ﺔ‬ ‫اﻟﻜﻠﯿ‬ ‫ﺔ‬ ‫اﻟﻤﻘﺎوﻣ‬ ‫ﻮن‬ ‫ﺗﻜ‬ ‫ﺚ‬ ‫ﺑﺤﯿ‬ ‫ﺔ‬ ‫ﻣﻘﻔﻠ‬ ‫ﺔ‬ ‫ﻛﮭﺮﺑﺎﺋﯿ‬ ‫ﺮة‬ ‫داﺋ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﺰء‬ ‫ﺟ‬ ‫ﻠﺔ‬ ‫اﻟﻤﻮﺻ‬ ‫ﺴﺎق‬ ‫اﻟ‬ ‫ﻮن‬ ‫ﺗﻜ‬ ‫ﺪﻣﺎ‬ ‫وﻋﻨ‬)R(‫ﺚ‬ ‫ﺣﯿ‬
)R‫اﻟﺮﺑﻂ‬ ‫واﺳﻼك‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺗﻤﺜﻞ‬(‫ﺎﻧﻮن‬‫ﻟﻘ‬ ‫ﺎ‬‫وﻓﻘ‬ ‫ﺴﺐ‬‫ﯾﺤ‬ ‫ﺪاﺋﺮة‬‫اﻟ‬ ‫ﺬه‬‫ھ‬ ‫ﻓﻲ‬ ‫ﻣﺤﺘﺚ‬ ‫ﺗﯿﺎر‬ ‫ﯾﻨﺴﺎب‬ ‫ﺳﻮف‬ ‫ﻟﺬﻟﻚ‬
‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اوم‬:
•‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻓﻲ‬ ‫اﻟﻀﺎﺋﻌﺔ‬ ‫او‬ ‫ﺪدة‬ ‫اﻟﻤﺘ‬ ‫اﻟﻘﺪرة‬ ‫اﻣﺎ‬)Pdissipated(‫اﻟ‬ ‫ﺔ‬‫اﻟﻤﻘﺎوﻣ‬ ‫ﻓﻲ‬ ‫ﺣﺮارة‬ ‫ﺑﮭﯿﺌﺔ‬ ‫ﺗﻈﮭﺮ‬ ‫واﻟﺘﻲ‬‫ﺔ‬‫ﻜﻠﯿ‬)R(
‫ﻟﻠﻌﻼﻗﺎت‬ ‫وﻓﻘﺎ‬ ‫ﻓﺘﺤﺴﺐ‬‫اﻻﺗﯿﺔ‬:
‫اﻟﻮاط‬ ‫ھﻲ‬ ‫اﻟﻤﺘﺒﺪدة‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﻘﺪرة‬ ‫ﻗﯿﺎس‬ ‫وﺣﺪة‬ ‫ﺣﯿﺚ‬)Watt(‫ﻟﮫ‬ ‫وﯾﺮﻣﺰ‬)W. (
•‫ﺛﺎﻧﯿﺔ‬ ‫ﻣﻐﻨﺎطﯿﺴﯿﺔ‬ ‫ﻗﻮة‬ ‫ﺗﺘﻮﻟﺪ‬ ‫ﺳﻮف‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻓﻲ‬ ‫ﻛﮭﺮﺑﺎﺋﻲ‬ ‫ﺗﯿﺎر‬ ‫ﻟﻤﺮور‬ ‫وﻧﺘﯿﺠﺔ‬)FB2(‫ﺎه‬‫وﺑﺎﺗﺠ‬ ‫اﻟﺴﺎق‬ ‫ﻋﻠﻰ‬ ‫ﻋﻤﻮدﯾﺔ‬ ‫وﺗﻜﻮن‬
‫ﻻﺗﺠ‬ ‫ﺎﻛﺲ‬‫ﻣﻌ‬‫ﺔ‬‫ﻣﺘﺒﺎطﺌ‬ ‫ﺔ‬‫اﻟﺤﺮﻛ‬ ‫ﻞ‬‫وﺗﺠﻌ‬ ‫ﺴﺎق‬‫اﻟ‬ ‫ﺔ‬‫ﺣﺮﻛ‬ ‫ﺔ‬‫ﻋﺮﻗﻠ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﻞ‬‫ﺗﻌﻤ‬ ‫ﺬﻟﻚ‬‫ﻟ‬ ‫ﻰ‬‫اﻟﯿﻤﻨ‬ ‫ﻒ‬‫اﻟﻜ‬ ‫ﺪة‬‫ﻗﺎﻋ‬ ‫ﺴﺐ‬‫ﺣ‬ ‫ﺔ‬‫اﻟﺤﺮﻛ‬ ‫ﺎه‬
)‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﻏﯿﺮ‬(‫اﻟﺘﺎﻟﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬ ‫اﻟﻘﻮة‬ ‫وﺗﺤﺴﺐ‬:
•‫ﺔ‬ ‫ﺧﺎرﺟﯿ‬ ‫ﻮة‬ ‫ﻗ‬ ‫ﺴﻠﯿﻂ‬ ‫ﺗ‬ ‫ﺐ‬ ‫ﯾﺘﻄﻠ‬ ‫ﺔ‬ ‫ﺛﺎﺑﺘ‬ ‫ﺴﺮﻋﺔ‬ ‫ﺑ‬ ‫ﺮك‬ ‫ﺗﺘﺤ‬ ‫ﺴﺎق‬ ‫اﻟ‬ ‫ﻞ‬ ‫ﻧﺠﻌ‬ ‫ﻲ‬ ‫وﻟﻜ‬)Fpull(‫اﻟ‬ ‫ﺴﺤﺐ‬ ‫ﺗ‬‫ﻮة‬ ‫اﻟﻘ‬ ‫ﺴﺎوي‬ ‫ﺗ‬ ‫ﻲ‬ ‫وھ‬ ‫ﺴﺎق‬
‫ان‬ ‫أي‬ ‫اﺗﺠﺎھﺎ‬ ‫وﺗﻌﺎﻛﺴﮭﺎ‬ ‫ﻣﻘﺪارا‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬:
2Bpull FF =
lBIF 2B =
R
B
Ior
R
I ind
motional
ind
lν
=
ε
=
R
PorIPorR.IP
2
motional
dissipatedmotionaldissipated
2
dissipated
ε
=ε==
θν=ε sinBmotional l

22. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-23-
∴
‫اﻟﻨﻴـﻮﺗﻦ‬ ‫ﻫـﻲ‬ ‫اﻟﺴﺎﺣﺒﺔ‬ ‫اﻟﺨﺎرﺟﻴﺔ‬ ‫اﻟﻘﻮة‬ ‫ﻗﻴﺎس‬ ‫وﺣﺪة‬ ‫ﺣﻴﺚ‬)N(‫ﺑﻮﺣـﺪ‬ ‫اﻟـﺪاﺋﺮة‬ ‫ﻓـﻲ‬ ‫اﻟﻤﻨـﺴﺎب‬ ‫اﻟﺘﻴـﺎر‬ ‫ﻳﻜـﻮن‬ ‫ﻋﻨـﺪﻣﺎ‬‫اﻣﺒﻴـﺮ‬ ‫ة‬
)A(‫ﺗﺴﻼ‬ ‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﻐﻨﺎﻃﻴﺴﻲ‬ ‫اﻟﻔﻴﺾ‬ ‫وﻛﺜﺎﻓﺔ‬)T(‫اﻟﻤﺘﺮ‬ ‫ﺑﻮﺣﺪة‬ ‫ﻣﻘﺎﺳﺔ‬ ‫اﻟﺴﺎق‬ ‫وﻃﻮل‬)m. (
‫اﻟﻌﻼﻗﺔ‬‫اﻟﻤﻐﻨﺎﻃﻴﺴﻲ‬ ‫اﻟﻔﻴﺾ‬ ‫ﺑﻴﻦ‬)ФB(‫اﻟﻤﻐﻨﺎﻃﻴﺴﻲ‬ ‫اﻟﻔﻴﺾ‬ ‫وﻛﺜﺎﻓﺔ‬)B(:
‫ﺴﻲ‬ ‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﯿﺾ‬ ‫اﻟﻔ‬ ‫ان‬‫ﺴﺎﺣﺔ‬ ‫ﻣ‬ ‫ﺮق‬ ‫ﯾﺨﺘ‬ ‫ﺬي‬ ‫اﻟ‬‫ﻄﺤﯿﺔ‬ ‫ﺳ‬‫ﺔ‬ ‫ﻣﻌﯿﻨ‬‫ﺘﺞ‬ ‫ﯾﻨ‬‫ﻲ‬ ‫اﻟﻨﻘﻄ‬ ‫ﻀﺮب‬ ‫اﻟ‬ ‫ﻞ‬ ‫ﺣﺎﺻ‬ ‫ﻦ‬ ‫ﻣ‬)‫ﻲ‬ ‫اﻟﻘﯿﺎﺳ‬(‫ﯿﻦ‬ ‫ﺑ‬‫ﮫ‬ ‫ﻣﺘﺠ‬
‫اﻟﻤﺴﺎﺣﺔ‬)
→
A(‫و‬‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻛﺜﺎﻓﺔ‬ ‫ﻣﺘﺠﮫ‬)
→
B(‫ان‬ ‫أي‬)
→→
=Φ B.AB(
‫اﻵﺗﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬ ‫ﻓﯿﺤﺴﺐ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﺗﻠﻚ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻣﻘﺪار‬ ‫اﻣﺎ‬:
‫ﺣﯿﺚ‬:
→
A:‫ﻣﺘﺠﮫ‬‫وھﻮ‬ ‫اﻟﻤﺴﺎﺣﺔ‬‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﻘﺎم‬ ‫اﻟﻌﻤﻮد‬)A(‫اﻟﺰاوﯾﺔ‬ ‫ﺿﻠﻌﻲ‬ ‫اﺣﺪ‬ ‫وﯾﻤﺜﻞ‬)θ(.
→
B:‫اﻟﺰاوﯾﺔ‬ ‫اﺿﻼع‬ ‫ﻣﻦ‬ ‫اﻻﺧﺮ‬ ‫اﻟﻀﻠﻊ‬ ‫وﯾﻤﺜﻞ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻛﺜﺎﻓﺔ‬ ‫ﻣﺘﺠﮫ‬)θ.(
A:‫اﻟﺴﻄﺢ‬ ‫ﻣﺴﺎﺣﺔ‬)‫او‬ ‫اﻟﺤﻠﻘﺔ‬ ‫ﻣﺴﺘﻮي‬‫اﻟﻤﻠﻒ‬ ‫ﻣﺴﺘﻮي‬(‫ﻗﯿﺎﺳﯿﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫وھﻲ‬)‫ﻣﻘﺪارﯾﺔ‬(‫ووﺣﺪﺗﮭﺎ‬)m2
(.
ФB:‫ھﻲ‬ ‫ووﺣﺪﺗﮫ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬Weber)wb(‫ﻗﯿﺎﺳﯿﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫وھﻮ‬)‫ﻣﻘﺪارﯾﺔ‬.(
B:‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻛﺜﺎﻓﺔ‬)‫او‬‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﺷﺪة‬(‫اﻻﺗﺠﺎھﯿﺔ‬ ‫اﻟﻜﻤﯿﺎت‬ ‫ﻣﻦ‬ ‫وھﻮ‬‫ووﺣﺪ‬‫ﺗﮫ‬Tesla)T(.
‫ﺣﯿﺚ‬)T=wb/m2
.(
θ:‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻣﺘﺠﮫ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺤﺼﻮرة‬ ‫اﻟﺰاوﯾﺔ‬ ‫ھﻲ‬)
→
A(‫وﻣﺘﺠﮫ‬‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻛﺜﺎﻓﺔ‬)
→
B. (
Bcosθ:‫ﻣﺮﻛﺒﺔ‬‫اﻟﺴﻄﺢ‬ ‫ﻣﺴﺎﺣﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﻤﻮدﯾﺔ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻛﺜﺎﻓﺔ‬)A.(
‫ﻣﻼﺣﻈﺎت‬/
1-‫ﻋﻨﺪﻣﺎ‬)
→→
⊥ BA(‫ﻓﺎن‬)θ=90 ͦ(‫وان‬)cos90 ͦ(‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬)ФB=0(‫ﺴﻄﺢ‬‫اﻟ‬ ‫ﺮق‬‫ﯾﺨﺘ‬ ‫ﺴﻲ‬‫ﻣﻐﻨﺎطﯿ‬ ‫ﯿﺾ‬‫ﻓ‬ ‫ﯾﺘﻮاﻓﺮ‬ ‫ﻻ‬ ‫أي‬
‫اﻟﺤﺎﻟ‬ ‫ھﺬه‬ ‫ﻓﻲ‬‫وﻋﻨﺪﻣﺎ‬ ، ‫ﺔ‬)
→
B//
→
A(‫ﻓﺎن‬)θ=0(‫وان‬)cos0=1(‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬)ФB=AB(‫ﯾﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻋﻈﻢ‬.
‫اﻟﺪاﺋﺮي‬ ‫اﻟﺴﻄﺢ‬ ‫ﻣﺴﺎﺣﺔ‬)‫ﺮي‬‫داﺋ‬ ‫ﺳﻠﻜﻲ‬ ‫ﻣﻠﻒ‬ ‫او‬ ‫ﻣﻮﺻﻠﺔ‬ ‫ﺣﻠﻘﺔ‬(‫ﺔ‬‫اﻟﺘﺎﻟﯿ‬ ‫ﺔ‬‫ﻟﻠﻌﻼﻗ‬ ‫ﺎ‬‫وﻓﻘ‬ ‫ﺴﺐ‬‫ﺗﺤ‬) :A=π r2
(‫ﺚ‬‫ﺣﯿ‬)r(‫ﺼﻒ‬‫ﻧ‬
‫اﻟﻘﻄﺮ‬.
2-‫ﻣﻦ‬ ‫ﻟﻠﺘﺤﻮﯾﻞ‬)cm2
(‫إﻟﻰ‬)m2
(‫ﻓﻲ‬ ‫اﻟﻤﻘﺪار‬ ‫ﻧﻀﺮب‬)10-4
.(
3-‫ﺴﻲ‬ ‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﯿﺾ‬ ‫اﻟﻔ‬ ‫ﺎس‬ ‫ﻟﻘﯿ‬ ‫ﺮى‬ ‫أﺧ‬ ‫ﺪة‬ ‫وﺣ‬ ‫ﻚ‬ ‫ھﻨﺎﻟ‬)ФB(‫ﺴﻮﯾﻞ‬ ‫اﻟﻤﺎﻛ‬ ‫ﻲ‬ ‫وھ‬)Maxwell(‫ﻦ‬ ‫ﻣ‬ ‫ﺪ‬ ‫واﺣ‬ ‫ﻂ‬ ‫ﺧ‬ ‫ﻞ‬ ‫ﯾﻤﺜ‬ ‫ﻮ‬ ‫وھ‬
‫ﻞ‬‫ﻛ‬ ‫وان‬ ‫ﺴﯿﺔ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﻮة‬‫اﻟﻘ‬ ‫ﺧﻄﻮط‬)wb=108
Maxwell(‫ﻲ‬‫ﻓ‬ ‫ﺪار‬‫اﻟﻤﻘ‬ ‫ﻀﺮب‬‫ﻧ‬ ‫ﺮ‬‫وﯾﺒ‬ ‫ﻰ‬‫إﻟ‬ ‫ﺴﻮﯾﻞ‬‫ﻣﺎﻛ‬ ‫ﻦ‬‫ﻣ‬ ‫ﻞ‬‫ﻟﻠﺘﺤﻮﯾ‬ ‫ﺬﻟﻚ‬‫ﻟ‬
)10-8
.(
6-‫ﺎ‬ ‫ﻣﻌﻄ‬ ‫ﺔ‬ ‫اﻟﺰاوﯾ‬ ‫ﺖ‬ ‫ﻛﺎﻧ‬ ‫اذا‬ ‫ﺴﺎﻟﺔ‬ ‫اﻟﻤ‬ ‫ﻲ‬ ‫ﻓ‬‫ة‬‫ﺴﺘﻮي‬ ‫ﻣ‬ ‫ﯿﻦ‬ ‫ﺑ‬‫ﺔ‬ ‫اﻟﺤﻠﻘ‬ ‫ﺴﺘﻮي‬ ‫ﻣ‬ ‫او‬ ‫ﻒ‬ ‫اﻟﻤﻠ‬‫و‬‫ﺎه‬ ‫اﺗﺠ‬‫ﺴﻲ‬ ‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﯿﺾ‬ ‫اﻟﻔ‬ ‫ﺔ‬ ‫ﻛﺜﺎﻓ‬
‫ﻋﻠﻰ‬ ‫ﻓﻠﻠﺤﺼﻮل‬‫اﻟﺰاوﯾﺔ‬)θ(‫ﺴﺎﺣﺔ‬‫اﻟﻤ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫ﺑﯿﻦ‬)
→
A(‫ﺴﻲ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﯿﺾ‬‫اﻟﻔ‬ ‫ﺔ‬‫ﻛﺜﺎﻓ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫و‬)
→
B(‫ﺎة‬‫اﻟﻤﻌﻄ‬ ‫ﺔ‬‫اﻟﺰاوﯾ‬ ‫ﺮح‬‫ﻧﻄ‬
‫ﻣﻦ‬ ‫اﻟﺴﺆال‬ ‫ﻓﻲ‬90ͦ)‫اﻟﻤﻌﻄﺎة‬ ‫اﻟﺰاوﯾﺔ‬ ‫ﻣﺘﻤﻤﺔ‬ ‫ﻧﺎﺧﺬ‬ ‫أي‬‫اﻟﺴﺆال‬ ‫ﻓﻲ‬(.
θ=Φ cosABB
R
B
ForBIF
22
pullpull
l
l
ν
==

23. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-24-
‫ﻓﺮاداي‬ ‫ﻗﺎﻧﻮن‬:‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫اﻟﻘﻮة‬ ‫ﻣﻘﺪار‬)εind(‫ﯾﺘﻨﺎﺳ‬ ‫ﻠﻜﻲ‬‫ﺳ‬ ‫ﻣﻠﻒ‬ ‫او‬ ‫ﻣﻮﺻﻠﺔ‬ ‫ﺣﻠﻘﺔ‬ ‫ﻓﻲ‬‫ﺐ‬‫ﺪل‬‫اﻟﻤﻌ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬
‫اﻟﻤﻠﻒ‬ ‫او‬ ‫اﻟﺤﻠﻘﺔ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻓﻲ‬ ‫ﻟﻠﺘﻐﯿﺮ‬ ‫اﻟﺰﻣﻨﻲ‬(.
‫و‬‫اﻻﺗﯿﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫ﺑﺎﻟﺼﯿﻐﺔ‬ ‫ﻓﺮاداي‬ ‫ﻗﺎﻧﻮن‬ ‫ﻋﻦ‬ ‫ﯾﻌﺒﺮ‬:
‫ﺣﯿﺚ‬:
indε:‫ﻮ‬‫ﻧﻤ‬ ‫ﺪ‬‫ﻋﻨ‬ ‫ﺎﻟﺒﺔ‬‫ﺳ‬ ‫ﺑﻘﻄﺒﯿﺔ‬ ‫وﺗﻜﻮن‬ ‫اﻟﺤﻠﻘﺔ‬ ‫او‬ ‫اﻟﺴﻠﻜﻲ‬ ‫اﻟﻤﻠﻒ‬ ‫طﺮﻓﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﻮﻟﺪة‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫اﻟﻘﻮة‬ ‫ﻣﻌﺪل‬
‫اﻟﻔﯿﺾ‬)‫اﻻﻗﺘﺮاب‬ ‫ﻋﻨﺪ‬(‫ﻣﻮﺟﺒﺔ‬ ‫ﺑﻘﻄﺒﯿﺔ‬ ‫وﺗﻜﻮن‬‫اﻟﻔﯿﺾ‬ ‫ﺗﻼﺷﻲ‬ ‫ﻋﻦ‬)‫اﻻﺑﺘﻌﺎد‬ ‫ﻋﻨﺪ‬(‫ﻓﻮﻟﻂ‬ ‫ووﺣﺪﺗﮭﺎ‬)V.(
N:‫اﻟﻠﻔﺎت‬ ‫ﻋﺪد‬)‫ﺣ‬‫ﯿﺚ‬N=1‫ﻟﻠﺤﻠﻘﺔ‬. (
t
B
∆
∆Φ
:‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻟﺘﻐﯿﺮ‬ ‫اﻟﺰﻣﻨﻲ‬ ‫اﻟﻤﻌﺪل‬)wb/s.(
B∆Φ:‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫ﺑﺎﻟﻔﯿﺾ‬ ‫اﻟﺘﻐﯿﺮ‬)wb(‫ﺣﯿﺚ‬)1B2BB Φ−Φ=∆Φ(
‫وﯾﻜﻮن‬‫ﺑﺎﻟﻔﯿﺾ‬ ‫اﻟﺘﻐﯿﺮ‬‫اﻟﻔﯿﺾ‬ ‫ﻧﻤﻮ‬ ‫ﻋﻨﺪ‬ ‫ﻣﻮﺟﺐ‬)‫اﻟﻔﯿﺾ‬ ‫ﺗﺰاﯾﺪ‬(‫ﻻن‬)ФB2 > ФB1(‫و‬‫ﻻن‬ ‫ﯿﺾ‬‫اﻟﻔ‬ ‫ﺗﻼﺷﻲ‬ ‫ﻋﻨﺪ‬ ‫ﺳﺎﻟﺐ‬ ‫ﯾﻜﻮن‬
)ФB2 < ФB1.(
‫ﺔ‬‫اﻟﺪاﻓﻌ‬ ‫ﻮة‬‫اﻟﻘ‬ ‫ان‬ ‫ﻲ‬‫ﺗﻌﻨ‬ ‫ﻲ‬‫وھ‬ ‫ﺔ‬‫اﻟﻤﺤﺘﺜ‬ ‫ﺔ‬‫اﻟﻜﮭﺮﺑﺎﺋﯿ‬ ‫ﺔ‬‫اﻟﺪاﻓﻌ‬ ‫ﻮة‬‫اﻟﻘ‬ ‫ﺔ‬‫ﻗﻄﺒﯿ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺔ‬‫ﻟﻠﺪﻻﻟ‬ ‫ﻲ‬‫ﻓﮭ‬ ‫ﺎﻧﻮن‬‫اﻟﻘ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺴﺎﻟﺒﺔ‬‫اﻟ‬ ‫ﺎرة‬‫اﻻﺷ‬ ‫ﺎ‬‫اﻣ‬
‫ﻟﻨﺰ‬ ‫ﻟﻘﺎﻧﻮن‬ ‫وﻓﻘﺎ‬ ‫وﻟﺪھﺎ‬ ‫اﻟﺬي‬ ‫او‬ ‫ﺣﺜﮭﺎ‬ ‫ﺳﺒﺐ‬ ‫اﻟﺬي‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫ﺑﺎﻟﻔﯿﺾ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫ﺗﻌﺎﻛﺲ‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬.
)cosAB(cosAB BB θ∆=∆Φ⇒θ=ΦQ
‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫ﺑﺎﻟﻔﯿﺾ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫ان‬ ‫ﺣﯿﺚ‬‫ﯾﺤﺼﻞ‬‫اﺛﻨﺎء‬ ‫اﻟﺰاوﯾﺔ‬ ‫ﺑﺘﻐﯿﺮ‬ ‫او‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﺑﺘﻐﯿﺮ‬ ‫او‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻛﺜﺎﻓﺔ‬ ‫ﺑﺘﻐﯿﺮ‬ ‫اﻣﺎ‬
‫ﻓﺎن‬ ‫وﺑﺎﻟﺘﺎﻟﻲ‬ ‫اﻟﺪوران‬:
)coscoscos()AAA()BBB(
)cos(ABorcos)A(Borcos)B(A
121212
BBB
θ−θ=θ∆−=∆−=∆
θ∆=∆Φθ∆=∆Φθ∆=∆Φ
‫اﺧﺮى‬ ‫ﺻﯿﻎ‬ ‫ﺛﻼث‬ ‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬ ‫ﻓﺮاداي‬ ‫ﻗﺎﻧﻮن‬ ‫ﻓﻲ‬ ‫اﻟﺘﻌﻮﯾﺾ‬ ‫وﺑﻌﺪ‬‫اﻟﻌﻮا‬ ‫ﻋﻠﻰ‬ ‫واﻋﺘﻤﺎدا‬ ‫ﻟﻠﻘﺎﻧﻮن‬‫اﻟﻔﯿﺾ‬ ‫ﻋﻠﯿﮭﺎ‬ ‫ﯾﻌﺘﻤﺪ‬ ‫اﻟﺘﻲ‬ ‫ﻣﻞ‬
‫وھﻲ‬:
•‫ﻦ‬‫ﻣ‬ ‫ﺰء‬‫ﺟ‬ ‫اﻟﻤﻠﻒ‬ ‫ﯾﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺎ‬‫ﻣﻘﺎوﻣﺘﮭ‬ ‫ﺔ‬‫ﻣﻘﻔﻠ‬ ‫ﺔ‬‫ﺧﺎرﺟﯿ‬ ‫ﺮة‬‫داﺋ‬)R()‫و‬‫ﻮع‬‫ﻣﺠﻤ‬ ‫ﻞ‬‫ﺗﻤﺜ‬‫ﺎت‬‫ﻣﻘﺎوﻣ‬‫ﺪاﺋﺮة‬‫اﻟ‬(‫ﺴﻮف‬‫ﻓ‬
‫اﻟﻤﺤﺘﺚ‬ ‫ﺑﺎﻟﺘﯿﺎر‬ ‫ﯾﺪﻋﻰ‬ ‫اﻟﺪاﺋﺮة‬ ‫ھﺬه‬ ‫ﻓﻲ‬ ‫ﺗﯿﺎر‬ ‫ﯾﻨﺴﺎب‬)Iind(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اوم‬ ‫ﻟﻘﺎﻧﻮن‬ ‫وﻓﻘﺎ‬ ‫ﯾﺤﺴﺐ‬:
t
N B
ind
∆
∆Φ
−=ε
R
I ind
ind
ε
=
‫ﻓﺮاداي‬ ‫ﻗﺎﻧﻮن‬
t
cos
NABorcos
t
A
NBorcos
t
B
NA indindind
∆
θ∆
−=εθ
∆
∆
−=εθ
∆
∆
−=ε

24. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-25-
‫ﻣﻼﺣﻈﺎت‬‫ﻓﺮاداي‬ ‫ﻗﺎﻧﻮن‬ ‫ﻋﻠﻰ‬:
1-‫ﻣﺤﺘﺜﺔ‬ ‫ﻛﮭﺮﺑﺎﺋﯿﺔ‬ ‫داﻓﻌﺔ‬ ‫ﻗﻮة‬ ‫ﺗﺘﻮﻟﺪ‬)εind(‫ﺴﻲ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﺎﻟﻔﯿﺾ‬‫ﺑ‬ ‫ﺮ‬‫ﻟﻠﺘﻐﯿ‬ ‫اﻟﺰﻣﻨﻲ‬ ‫اﻟﻤﻌﺪل‬ ‫ﻛﺎن‬ ‫ﻛﻠﻤﺎ‬ ‫اﻛﺒﺮ‬ ‫ﺑﻤﻘﺪار‬)
t
B
∆
∆Φ
(
‫ﻛﺒﯿﺮا‬ ‫اﻟﻤﻠﻒ‬ ‫او‬ ‫اﻟﺤﻠﻘﺔ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(‫اﻟﻤﻠﻒ‬ ‫ﻟﻔﺎت‬ ‫ﻋﺪد‬ ‫زاد‬ ‫ﻛﻠﻤﺎ‬ ‫او‬)N) (‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬(.
2-‫ا‬ ‫ﯾﻜﻮن‬‫ﺴﻲ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﻟﻔﯿﺾ‬)ФB(‫ﺪاره‬‫ﻣﻘ‬ ‫ﻲ‬‫ﻓ‬‫ﻢ‬‫اﻷﻋﻈ‬‫ﻰ‬‫ﻋﻠ‬ ‫ﺎ‬‫ﻋﻤﻮدﯾ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫او‬ ‫ﻠﺔ‬‫اﻟﻤﻮﺻ‬ ‫ﺔ‬‫اﻟﺤﻠﻘ‬ ‫ﺴﺘﻮي‬‫ﻣ‬ ‫ﻮن‬‫ﯾﻜ‬ ‫ﺪﻣﺎ‬‫ﻋﻨ‬
‫ﺴﻲ‬ ‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﯿﺾ‬ ‫اﻟﻔ‬ ‫ﺪم‬ ‫وﯾﻨﻌ‬ ‫ﺴﻲ‬ ‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﺎل‬ ‫اﻟﻤﺠ‬)ФB=0(‫ﺎل‬ ‫ﻟﻠﻤﺠ‬ ‫ﺎ‬ ‫ﻣﻮازﯾ‬ ‫ﻒ‬ ‫اﻟﻤﻠ‬ ‫او‬ ‫ﺔ‬ ‫اﻟﺤﻠﻘ‬ ‫ﺴﺘﻮي‬ ‫ﻣ‬ ‫ﺼﺒﺢ‬ ‫ﯾ‬ ‫ﺪﻣﺎ‬ ‫ﻋﻨ‬
‫او‬ ‫دورة‬ ‫رﺑﻊ‬ ‫اﻟﻤﻠﻒ‬ ‫ﯾﺪور‬ ‫ﻋﻨﺪﻣﺎ‬ ‫أي‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬90º‫او‬rad
2
π
.
3-‫اﻟﺬي‬ ‫اﻟﻮﺿﻊ‬ ‫ﻣﻦ‬ ‫اﻟﻤﻠﻒ‬ ‫او‬ ‫اﻟﺤﻠﻘﺔ‬ ‫ﺗﺪور‬ ‫ﻋﻨﺪﻣﺎ‬‫ﺴﺘﻮاھﺎ‬‫ﻣ‬ ‫ﻮن‬‫ﯾﻜ‬ ‫ﺬي‬‫اﻟ‬ ‫ﻊ‬‫اﻟﻮﺿ‬ ‫ﻰ‬‫إﻟ‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫ﻋﻠﻰ‬ ‫ﻋﻤﻮدي‬ ‫ﻣﺴﺘﻮاھﺎ‬ ‫ﯾﻜﻮن‬
‫ﺎل‬ ‫ﻟﻠﻤﺠ‬ ‫ﻮاز‬ ‫ﻣ‬)‫دورة‬ ‫ﻊ‬ ‫رﺑ‬ ‫ﻒ‬ ‫اﻟﻤﻠ‬ ‫او‬ ‫ﺔ‬ ‫اﻟﺤﻠﻘ‬ ‫ﺪور‬ ‫ﺗ‬ ‫ﺪﻣﺎ‬ ‫ﻋﻨ‬ ‫أي‬(‫ﺔ‬ ‫اﻟﺤﺎﻟ‬ ‫ﺬه‬ ‫ھ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺴﻲ‬ ‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﯿﺾ‬ ‫اﻟﻔ‬ ‫ﻰ‬ ‫ﯾﺘﻼﺷ‬
)‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﯾﻨﻌﺪم‬. (
4-‫ﻓ‬ ‫وردت‬ ‫اذا‬‫اﻻﺗﯿﺔ‬ ‫اﻟﻌﺒﺎرات‬ ‫اﺣﺪى‬ ‫اﻟﺴﺆال‬ ‫ﻲ‬)‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﺐ‬‫ﻗﻠ‬ ‫او‬ ‫دورة‬ ‫ﺼﻒ‬‫ﻧ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫دار‬ ‫او‬ ‫ﺎل‬‫اﻟﻤﺠ‬ ‫اﻧﻌﻜﺲ‬(‫ﺎد‬‫ﻻﯾﺠ‬ ‫ﺎن‬‫ﻓ‬
)indε(‫طﺮﯾﻘﺘﯿﻦ‬:
‫اﻟﺼﯿﻐﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫ھﻲ‬ ‫اﻻوﻟﻰ‬ ‫اﻟﻄﺮﯾﻘﺔ‬)θ
∆
∆
−=ε cos
t
B
NAind(‫ﺔ‬‫اﻟﺤﺎﻟ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺴﻲ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﯿﺾ‬‫اﻟﻔ‬ ‫ﺔ‬‫ﻛﺜﺎﻓ‬ ‫ﻞ‬‫ﺑﺠﻌ‬ ‫وذﻟﻚ‬
‫ﯿﺾ‬ ‫اﻟﻔ‬ ‫ﺔ‬ ‫ﻛﺜﺎﻓ‬ ‫ﺴﺎوي‬ ‫ﺗ‬ ‫ﺔ‬ ‫اﻟﺜﺎﻧﯿ‬‫ان‬ ‫أي‬ ‫ﺎ‬ ‫اﺗﺠﺎھ‬ ‫ﺴﮭﺎ‬ ‫وﺗﻌﺎﻛ‬ ‫ﺪارا‬ ‫ﻣﻘ‬ ‫ﻰ‬ ‫اﻻوﻟ‬ ‫ﺔ‬ ‫اﻟﺤﺎﻟ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺴﻲ‬ ‫اﻟﻤﻐﻨﺎطﯿ‬)12 BB −=(‫ﺎن‬ ‫ﻓ‬ ‫ﺬﻟﻚ‬ ‫ﻟ‬
)ΔB=-2B. (
‫اﻟﺼﯿﻐﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫ھﻲ‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫اﻟﻄﺮﯾﻘﺔ‬)
t
cos
NABind
∆
θ∆
−=ε(‫ﺴﺎوي‬‫ﺗ‬ ‫ﺎﻧﻲ‬‫اﻟﺜ‬ ‫ﻊ‬‫اﻟﻮﺿ‬ ‫ﺔ‬‫زاوﯾ‬ ‫ﺑﺠﻌﻞ‬ ‫وذﻟﻚ‬180ͦ‫أي‬
‫ان‬)°=θ 1802. (
‫اﻟﻜﻬﺮﺑﺎﺋ‬ ‫اﻟﻤﻮﻟﺪ‬‫ﻲ‬:‫ﻛﮭﺮﺑﺎﺋﯿﺔ‬ ‫طﺎﻗﺔ‬ ‫إﻟﻰ‬ ‫اﻟﻤﯿﻜﺎﻧﯿﻜﯿﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺗﺤﻮﯾﻞ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻌﻤﻞ‬ ‫ﺟﮭﺎز‬ ‫ھﻮ‬‫ﻣﻐﻨﺎطﯿﺴﻲ‬ ‫ﻣﺠﺎل‬ ‫ﺑﺘﺄﺛﯿﺮ‬.
♦‫ﻓ‬‫ﻌﻨﺪ‬‫ﯾﺪور‬ ‫ﻣﺎ‬‫ﺪ‬‫اﻟﻤﻮﻟ‬ ‫ﻮاة‬‫ﻧ‬ ‫ﻣﻠﻒ‬‫ﮫ‬‫ﻟﻔﺎﺗ‬ ‫ﺪد‬‫ﻋ‬ ‫ﺬي‬‫واﻟ‬)N(‫ﺪة‬‫اﻟﻮاﺣ‬ ‫ﺔ‬‫اﻟﻠﻔ‬ ‫ﺴﺎﺣﺔ‬‫وﻣ‬)A) (‫ﺪة‬‫ﺑﻮﺣ‬m2
(‫ﺔ‬‫زاوﯾ‬ ‫ﺴﺮﻋﺔ‬‫ﺑ‬)ω(
‫ﺔ‬‫ﻣﻨﺘﻈﻤ‬)‫ﺪة‬‫ﺑﻮﺣ‬rad/sec(‫ﺴﻲ‬‫ﻣﻐﻨﺎطﯿ‬ ‫ﺎل‬‫ﻣﺠ‬ ‫ﻲ‬‫وﻓ‬‫ﻀﮫ‬‫ﻓﯿ‬ ‫ﺔ‬‫ﻛﺜﺎﻓ‬)B(‫ﺔ‬‫ﻣﻨﺘﻈﻤ‬‫ﺪة‬‫ﺑﻮﺣ‬)T(‫ﺴﻲ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﯿﺾ‬‫اﻟﻔ‬ ‫ﺎن‬‫ﻓ‬
‫ﺎ‬‫دورﯾ‬ ‫ﺮ‬‫ﯾﺘﻐﯿ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺪة‬‫اﻟﻮاﺣ‬ ‫ﺔ‬‫اﻟﻠﻔ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬‫ﺔ‬‫ﻣﺤﺘﺜ‬ ‫ﺔ‬‫ﻓﻮﻟﻄﯿ‬ ‫ﺪ‬‫ﺗﺘﻮﻟ‬ ‫ﺬﻟﻚ‬‫ﻟ‬ ‫ﺰﻣﻦ‬‫اﻟ‬ ‫ﻊ‬‫ﻣ‬‫ﺔ‬‫آﻧﯿ‬‫ﺪﻋﻰ‬‫ﺗ‬ ‫ﺔ‬‫اﻟﻤﻮﺟ‬ ‫ﺔ‬‫ﺟﯿﺒﯿ‬
‫ﺗﻤﺘﺎز‬ ‫واﻟﺘﻲ‬ ‫اﻟﻤﺘﻨﺎوﺑﺔ‬ ‫ﺑﺎﻟﻔﻮﻟﻄﯿﺔ‬‫ﺑﺄﻧﮭﺎ‬‫اﻟﺰﻣ‬ ‫ﻣﻊ‬ ‫دورﯾﺎ‬ ‫واﺗﺠﺎھﺎ‬ ‫ﻣﻘﺪارا‬ ‫ﺗﺘﻐﯿﺮ‬‫ﻦ‬.
‫اﻻﻧﯿﺔ‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﻋﻦ‬ ‫وﯾﻌﺒﺮ‬)‫اﻟﻠﺤﻈﯿﺔ‬(‫اﻟ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬‫اﻻﺗﯿﺔ‬ ‫ﺮﯾﺎﺿﯿﺔ‬:
,
‫ﺣﯿﺚ‬:
εins:‫اﻟﻤﻘﺪار‬‫اﻵﻧﻲ‬‫اﻟﻤﺤﺘﺜﺔ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬)‫ﻓﻲ‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬‫أﯾﺔ‬‫ﻟﺤﻈﺔ‬(.
εmax:‫اﻟﻤﻘﺪار‬‫اﻷﻋﻈﻢ‬‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬)‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ذروة‬(‫اﻻﺗﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬ ‫وﯾﺤﺴﺐ‬:
,
tω:‫اﻟﻄﻮر‬ ‫زاوﯾﺔ‬)‫اﻻزاﺣﺔ‬ ‫زاوﯾﺔ‬(‫ﺑﻮﺣﺪة‬rad.
f:‫ھﺮﺗﺰ‬ ‫ﺑﻮﺣﺪة‬ ‫وﯾﻘﺎس‬ ‫اﻟﺘﺮدد‬)Hertz(‫ﻟﮫ‬ ‫وﯾﺮﻣﺰ‬)Hz(‫ﺣﯿﺚ‬)Hz=1/sec(.
‫ﺎ‬‫طﺮﻓ‬ ‫ﺮﺑﻂ‬‫ﯾ‬ ‫ﺪﻣﺎ‬‫وﻋﻨ‬‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺎ‬‫ﻣﻘﺎوﻣﺘﮭ‬ ‫ﺔ‬‫ﺧﺎرﺟﯿ‬ ‫ﺮة‬‫داﺋ‬ ‫ﻰ‬‫إﻟ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﺬا‬‫ھ‬)R(‫ﯾﺘﻮ‬‫ﻲ‬‫آﻧ‬ ‫ﺚ‬‫ﻣﺤﺘ‬ ‫ﺎر‬‫ﺗﯿ‬ ‫ﺪ‬‫ﻟ‬)‫ﻲ‬‫ﻟﺤﻈ‬(‫ﻲ‬‫ﺟﯿﺒ‬
‫اﻟﺘﺎﻟﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫وﯾﻌﻄﻰ‬ ‫اﻟﺰﻣﻦ‬ ‫ﻣﻊ‬ ‫دورﯾﺎ‬ ‫واﺗﺠﺎھﺎ‬ ‫ﻣﻘﺪارا‬ ‫ﻣﺘﻐﯿﺮ‬ ‫ﺑﺄﻧﮫ‬ ‫ﯾﻤﺘﺎز‬ ‫واﻟﺬي‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫ﺑﺎﻟﺘﯿﺎر‬ ‫ﯾﺪﻋﻰ‬ ‫اﻟﻤﻮﺟﺔ‬:
f2π=ωBNAmax ω=ε
)tsin(maxins ωε=ε

25. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-26-
‫اﻟﺘﯿﺎر‬ ‫ﺣﺴﺎب‬ ‫ﯾﻤﻜﻦ‬ ‫ﻛﺬﻟﻚ‬‫اﻵﻧﻲ‬)Iins(‫اﻟﺘﯿﺎر‬ ‫او‬‫اﻷﻋﻈﻢ‬)Im(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اوم‬ ‫ﻟﻘﺎﻧﻮن‬ ‫وﻓﻘﺎ‬:
‫ﺔ‬‫اﻟﻤﻘﺎوﻣ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺎر‬‫اﻟﺘﯿ‬ ‫ﻊ‬‫ﻣﺮﺑ‬ ‫ﺮب‬‫ﺿ‬ ‫ﺣﺎﺻﻞ‬ ‫ﻣﻦ‬ ‫او‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﻓﻲ‬ ‫اﻟﺘﯿﺎر‬ ‫ﺿﺮب‬ ‫ﺣﺎﺻﻞ‬ ‫ﻣﻦ‬ ‫ﺗﻨﺘﺞ‬ ‫اﻟﻘﺪرة‬ ‫ان‬ ‫وﺑﻤﺎ‬‫ﺴﻤﺔ‬‫ﻗ‬ ‫ﻦ‬‫ﻣ‬ ‫او‬
‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﻣﺮﺑﻊ‬‫ﻟﺬﻟﻚ‬‫ﻟﺤ‬‫اﻟﻌﻼﻗﺎت‬ ‫ﻧﺴﺘﺨﺪم‬ ‫اﻻﻧﯿﺔ‬ ‫اﻟﻘﺪرة‬ ‫ﺴﺎب‬‫اﻻﺗﯿﺔ‬:
‫اﻟﻘﺪرة‬ ‫ﻟﺤﺴﺎب‬ ‫اﻣﺎ‬‫اﻟﻌﻈﻤﻰ‬)Pmax(‫اﻟﻌﻼﻗ‬ ‫ﻓﻨﺴﺘﺨﺪم‬‫ﺎت‬‫اﻻﺗﯿﺔ‬:
‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻇﺎﻫﺮة‬:‫ﺪة‬‫وﺣ‬ ‫ﻼل‬‫ﺧ‬ ‫ﮫ‬‫ﻓﯿ‬ ‫ﺎر‬‫اﻟﻤ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻟﺘﻐﯿﺮ‬ ‫ﻧﺘﯿﺠﺔ‬ ‫ﻣﻠﻒ‬ ‫ﻓﻲ‬ ‫ذاﺗﯿﺔ‬ ‫ﻣﺤﺘﺜﺔ‬ ‫ﻛﮭﺮﺑﺎﺋﯿﺔ‬ ‫داﻓﻌﺔ‬ ‫ﻗﻮة‬ ‫ﺗﻮﻟﯿﺪ‬ ‫ظﺎھﺮة‬ ‫ھﻲ‬
‫اﻟﺰﻣﻦ‬.
‫ﺣﺴﺎب‬‫اﻟﺬاﺗﻴﺔ‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﻬﺮﺑﺎﺋﻴﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫اﻟﻘﻮة‬)εind(‫اﻟﻤﻠﻒ‬ ‫ﻓﻲ‬:
‫اﻟﻘ‬ ‫ان‬‫اﻟﻜﮭﺮﺑ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫ﻮة‬‫ﻲ‬‫طﺮﻓ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﻮﻟﺪة‬ ‫اﻟﺬاﺗﯿﺔ‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫ﺎﺋﯿﺔ‬‫ﮫ‬‫ﻓﯿ‬ ‫ﺴﺎب‬‫اﻟﻤﻨ‬ ‫ﺎر‬‫اﻟﺘﯿ‬ ‫ﺮ‬‫ﻟﺘﻐﯿ‬ ‫ﺔ‬‫ﻧﺘﯿﺠ‬ ‫ﻒ‬‫اﻟﻤﻠ‬)‫ﻲ‬‫ﻓ‬ ‫ﺎر‬‫اﻟﺘﯿ‬ ‫ﺮ‬‫ﺗﻐﯿ‬
‫اﻟﻤﻠﻒ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬ ‫اﻟﻤﻐﻨﺎطﯿﺲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﻓﻲ‬ ‫ﺗﻐﯿﺮ‬ ‫ﺣﺼﻮل‬ ‫ﻓﻲ‬ ‫ﯾﺘﺴﺒﺐ‬ ‫اﻟﻤﻠﻒ‬(‫اﻵﺗﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬ ‫ﺗﺤﺴﺐ‬:
‫ﺣﯿﺚ‬:
εind:‫ﻋﻨﺪ‬ ‫ﺳﺎﻟﺒﺔ‬ ‫ﻗﻄﺒﯿﺘﮭﺎ‬ ‫وﺗﻜﻮن‬ ‫اﻟﺬاﺗﯿﺔ‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫اﻟﻘﻮة‬‫ﺪاره‬‫ﻣﻘ‬ ‫ﻰ‬‫اﻟ‬ ‫اﻟﺼﻔﺮ‬ ‫ﻣﻦ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻧﻤﻮ‬‫ﻮن‬‫وﺗﻜ‬ ‫ﻢ‬‫اﻻﻋﻈ‬
‫ﻗﻄﺒﯿﺘﮭﺎ‬‫ﻣﻮﺟﺒﺔ‬‫اﻟﺼﻔﺮ‬ ‫اﻟﻰ‬ ‫اﻻﻋﻈﻢ‬ ‫اﻟﻤﻘﺪار‬ ‫ﻣﻦ‬ ‫اﻟﺘﯿﺎر‬ ‫ﺗﻼﺷﻲ‬ ‫ﻋﻨﺪ‬.
L:‫ﺮ‬‫ﺑﺘﻐﯿ‬ ‫اﻻ‬ ‫ﺮ‬‫ﯾﺘﻐﯿ‬ ‫ﻻ‬ ‫ﺪ‬‫اﻟﻮاﺣ‬ ‫ﻒ‬‫ﻟﻠﻤﻠ‬ ‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﻮ‬‫وھ‬ ‫ﻒ‬‫ﻣﻠ‬ ‫ﻞ‬‫ﻛ‬ ‫ﺧﻮاص‬ ‫ﻣﻦ‬ ‫ﺧﺎﺻﯿﺔ‬ ‫وھﻮ‬ ‫ﻟﻠﻤﻠﻒ‬ ‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬‫ﻮاص‬‫ﺧ‬
‫داﺋﻤﺎ‬ ‫ﻣﻮﺟﺐ‬ ‫وﯾﻜﻮن‬ ‫اﻟﻤﻠﻒ‬ ‫ذﻟﻚ‬.‫ﺑﺎﻧﮫ‬ ‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫وﯾﻌﺮف‬)‫ﻧﺴﺒﺔ‬‫إ‬ ‫ﻒ‬‫ﻣﻠ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺤﺘﺜ‬ ‫ﺔ‬‫اﻟﻜﮭﺮﺑﺎﺋﯿ‬ ‫ﺔ‬‫اﻟﺪاﻓﻌ‬ ‫ﻮة‬‫اﻟﻘ‬‫ﻰ‬‫ﻟ‬
‫ﻓﻲ‬ ‫اﻟﻤﻨﺴﺎب‬ ‫اﻟﺘﯿﺎر‬ ‫ﻟﺘﻐﯿﺮ‬ ‫اﻟﺰﻣﻨﻲ‬ ‫اﻟﻤﻌﺪل‬‫ﻧﻔﺴﮫ‬ ‫اﻟﻤﻠﻒ‬(.
‫اﻵﺗﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬ ‫ﯾﺤﺴﺐ‬ ‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫ﻓﺎن‬ ‫اﻟﺘﻌﺮﯾﻒ‬ ‫ھﺬا‬ ‫ﺑﻤﻮﺟﺐ‬ ‫ﻟﺬﻟﻚ‬:
‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫وﯾﻘﺎس‬)L(‫اﻟﮭﻨﺮي‬ ‫ﺑﻮﺣﺪة‬ ‫ﻟﻠﻮﺣﺪات‬ ‫اﻟﺪوﻟﻲ‬ ‫اﻟﻨﻈﺎم‬ ‫ﻓﻲ‬)Henry(‫وﺗﺨﺘﺼﺮ‬)H(
t
I
L ind
∆
∆
ε
−=
R
porRIPorIP
2
max
max
2
maxmaxmaxmaxmax
ε
==ε=
R
PorRIPorIP
2
ins
ins
2
insinsinsinsins
ε
==ε=
t
I
Lind
∆
∆
−=ε
R
I,
R
I max
max
ins
ins
ε
=
ε
=
)tsin(II maxins ω=
‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻗﺎﻧﻮن‬
‫ﺗﻌﺮﻳﻔﻪ‬ ‫ﺑﻤﻮﺟﺐ‬ ‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫ﺣﺴﺎب‬

26. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-27-
‫ﺣﯿﺚ‬:Henry =Volt. second/Ampere
‫اﻟﻤﻠﻲ‬ ‫ﻣﺜﻞ‬ ‫اﻟﮭﻨﺮي‬ ‫أﺟﺰاء‬ ‫وھﻨﺎﻟﻚ‬‫ھﻨﺮي‬)mH(‫واﻟﻤﺎﯾﻜﺮوھﻨﺮي‬)μH. (
)
t
I
∆
∆
(:‫ﺑﻮﺣﺪة‬ ‫اﻟﺘﯿﺎر‬ ‫ﻟﺘﻐﯿﺮ‬ ‫اﻟﺰﻣﻨﻲ‬ ‫اﻟﻤﻌﺪل‬)A/s.(
ΔI:‫ﺣﯿﺚ‬ ‫ﺑﺎﻟﺘﯿﺎر‬ ‫اﻟﺘﻐﯿﺮ‬)ΔI=I2 – I1(‫و‬‫ﯾﻜﻮن‬‫اﻟﺘﻐﯿﺮ‬ ‫ھﺬا‬‫ﺎر‬‫اﻟﺘﯿ‬ ‫ﻮ‬‫ﻧﻤ‬ ‫ﺪ‬‫ﻋﻨ‬ ‫ﺐ‬‫ﻣﻮﺟ‬)‫ﺪ‬‫ﺗﺰاﯾ‬‫ﺎر‬‫اﻟﺘﯿ‬(‫ﻻن‬)I2 > I1(‫ﺎﻟﺐ‬‫وﺳ‬
‫اﻟﺘﯿﺎر‬ ‫ﺗﻼﺷﻲ‬ ‫ﻋﻨﺪ‬)‫اﻟﺘﯿﺎر‬ ‫ﺗﻨﺎﻗﺺ‬(‫ﻻن‬)I2 < I1(.
‫ﻣﻼﺣﻈ‬‫ﺎت‬/
1-‫اﺗﺠﺎه‬ ‫ﯾﻨﻌﻜﺲ‬ ‫ﻋﻨﺪﻣﺎ‬‫ﻓﺎن‬ ‫اﻟﺘﯿﺎر‬‫اﻟﺜﺎﻧﯿﺔ‬ ‫اﻟﺤﺎﻟﺔ‬ ‫ﺗﯿﺎر‬)I2(‫ﻰ‬‫اﻻوﻟ‬ ‫ﺔ‬‫اﻟﺤﺎﻟ‬ ‫ﺗﯿﺎر‬ ‫ﯾﺴﺎوي‬)I1(‫ان‬ ‫أي‬ ‫ﺎ‬‫اﺗﺠﺎھ‬ ‫ﺴﮫ‬‫وﯾﻌﺎﻛ‬ ‫ﺪارا‬‫ﻣﻘ‬
)I2=-I1(‫ﻓﺎن‬ ‫وﻣﻨﮭﺎ‬)ΔI=-2I.(
2-‫اﻻﻋﻈﻢ‬ ‫ﻣﻘﺪاره‬ ‫اﻟﺘﯿﺎر‬ ‫ﯾﺒﻠﻎ‬ ‫ﻋﻨﺪﻣﺎ‬)‫اﻟﺜﺎﺑﺖ‬(‫ﻓﺎن‬)εind =0. (
3-‫ﻣﻘﺪار‬)εind(‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫ﯾﺘﻨﺎﺳﺐ‬‫اﻟﻤﻌﺪل‬‫اﻟﺰﻣﻨﻲ‬‫ﻟ‬‫ﺑﺎﻟﺘﯿﺎر‬ ‫ﻠﺘﻐﯿﺮ‬‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫ﺑﺜﺒﻮت‬.
‫اﻟﺤﺜﻴﺔ‬ ‫اﻟﺪاﺋﺮة‬:
‫اﻟﺪ‬ ‫ﻓﻲ‬‫اﺋﺮ‬‫ة‬‫ﻓﺎن‬ ‫اﻟﺤﺜﯿﺔ‬:
Vapp:‫ﻓﻮﻟﻂ‬ ‫ﺑﻮﺣﺪة‬ ‫ﻣﺴﺘﻤﺮة‬ ‫ﻓﻮﻟﻄﯿﺔ‬ ‫وھﻲ‬ ‫اﻟﻤﺼﺪر‬ ‫ﻓﻮﻟﻄﯿﺔ‬ ‫او‬ ‫اﻟﻤﻄﺒﻘﺔ‬ ‫او‬ ‫اﻟﻤﻮﺿﻮﻋﺔ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬.
Vnet:‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﺻﺎﻓﻲ‬)‫ﻋﻠ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫او‬‫اﻟﻤﻘﺎوﻣﺔ‬ ‫طﺮﻓﻲ‬ ‫ﻰ‬.(
‫ا‬ ‫اﻟﻘﻮة‬ ‫ﻋﻦ‬ ‫اﻟﺘﻌﻮﯾﺾ‬ ‫وﺑﻌﺪ‬‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫ﻟﺪاﻓﻌﺔ‬)εind(‫اﻵﺗﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫إﺣﺪى‬ ‫ﻣﻦ‬:
t
I
Lind
∆
∆
=ε or
t
N B
ind
∆
∆Φ
=ε
‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﺻﺎﻓﻲ‬ ‫ﻋﻦ‬ ‫واﻟﺘﻌﻮﯾﺾ‬)Vnet(‫ﺣﯿﺚ‬ ‫اوم‬ ‫ﻗﺎﻧﻮن‬ ‫ﻣﻦ‬) :Vnet =Iins . R(‫اﻟﻤﻌﺎدﻟﺔ‬ ‫ﺗﺼﺒﺢ‬:
R:‫اﻟﻤﻠﻒ‬ ‫ﻣﻘﺎوﻣﺔ‬.
Iins:‫اﻻﻋﻈﻢ‬ ‫اﻟﻤﻘﺪار‬ ‫اﻟﻰ‬ ‫اﻟﺼﻔﺮ‬ ‫ﻣﻦ‬ ‫ﯾﺘﻐﯿﺮ‬ ‫وﻣﻘﺪاره‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻓﻲ‬ ‫اﻻﻧﻲ‬ ‫اﻟﺘﯿﺎر‬)‫اﻟﺜﺎﺑﺖ‬(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬:
♦‫اﻟﻤﻔﺘﺎح‬ ‫ﻏﻠﻖ‬ ‫ﻟﺤﻈﺔ‬) :Iins=0(‫و‬)indε‫ﯾﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻋﻈﻢ‬ ‫ﺗﻜﻮن‬(‫ﻟﺬﻟﻚ‬:
Vapp = ε ind ⇒
t
NVor
t
I
LV B
appapp
∆
∆Φ
=
∆
∆
=
♦‫ﻏﻠﻖ‬ ‫ﺑﻌﺪ‬‫ﻓﺎن‬ ‫ﺑﻠﺤﻈﺎت‬ ‫اﻟﻤﻔﺘﺎح‬‫ﺗﻄﺒﻖ‬ ‫اﻟﻤﻌﺎدﻟﺔ‬‫ﻻن‬ ‫ﻛﺎﻣﻠﺔ‬)0II( insconst >>‫ﻟﺬﻟﻚ‬:
t
NRIVor
t
I
LRIV B
insappinsapp
∆
∆Φ
+=
∆
∆
+=
t
NRIVor
t
I
LRIV B
insappinsapp
∆
∆Φ
+=
∆
∆
+=
indnetapp VV ε+= ‫اﻟﺤﺜﻴﺔ‬ ‫ﻟﻠﺪاﺋﺮة‬ ‫اﻟﻌﺎﻣﺔ‬ ‫اﻟﻤﻌﺎدﻟﺔ‬

27. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-28-
‫اﻻﺗﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺎت‬ ‫اﻻﻧﻲ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻋﻦ‬ ‫ﯾﻌﺒﺮ‬ ‫اﯾﻀﺎ‬ ‫اﻟﺤﺎﻟﺔ‬ ‫ھﺬه‬ ‫وﻓﻲ‬:
(‫اﻟﻤﻘﺪار‬ ‫ﻣﻌﻠﻮﻣﺔ‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫اﻟﻘﻮة‬ ‫ﺗﻜﻮن‬ ‫)ﻋﻨﺪﻣﺎ‬
or
‫اﻻﻋﻈﻢ‬ ‫ﻣﻘﺪاره‬ ‫ﻣﻦ‬ ‫ﻣﺌﻮﯾﺔ‬ ‫ﻧﺴﺒﺔ‬ ‫اﻟﺘﯿﺎر‬ ‫ﯾﻌﻄﻰ‬ ‫ﻋﻨﺪﻣﺎ‬)‫اﻟﺜﺎﺑﺖ‬ ‫ﻣﻘﺪاره‬(
♦‫اﻻﻋﻈﻢ‬ ‫ﻣﻘﺪاره‬ ‫اﻟﺘﯿﺎر‬ ‫ﯾﺒﻠﻎ‬ ‫ﻋﻨﺪﻣﺎ‬)‫اﻟﺜﺎﺑﺖ‬(‫اﻟﻤﻔﺘﺎح‬ ‫ﻏﻠﻖ‬ ‫ﻣﻦ‬ ‫ﻣﺪة‬ ‫ﺑﻌﺪ‬ ‫وذﻟﻚ‬‫أي‬)Iins = Iconst(‫ﻓﺎن‬)εind =0(‫ﻟﺬﻟﻚ‬:
‫اﻣﺎ‬)εind(‫اﻻﻋﻈﻢ‬ ‫اﻟﻤﻘﺪار‬ ‫ﻣﻦ‬ ‫ﯾﺘﻐﯿﺮ‬ ‫ﻣﻘﺪارھﺎ‬ ‫ﻓﺎن‬)‫ﺎح‬‫اﻟﻤﻔﺘ‬ ‫ﻏﻠﻖ‬ ‫ﻟﺤﻈﺔ‬(‫ﺼﻔﺮ‬‫اﻟ‬ ‫ﻰ‬‫اﻟ‬)‫ﺖ‬‫اﻟﺜﺎﺑ‬ ‫ﺪاره‬‫ﻣﻘ‬ ‫ﺎر‬‫اﻟﺘﯿ‬ ‫ﻮل‬‫وﺻ‬ ‫ﺪ‬‫ﻋﻨ‬(
‫اﻟﻤﻔﺘﺎح‬ ‫ﻏﻠﻖ‬ ‫ﻣﻦ‬ ‫ﻣﺪة‬ ‫ﺑﻌﺪ‬ ‫وذﻟﻚ‬‫اﻻﺗﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫اﺣﺪى‬ ‫ﻣﻦ‬ ‫ﺗﺤﺴﺐ‬ ‫ﻓﮭﻲ‬ ‫ﻟﺬﻟﻚ‬:
εind = Vapp ‫اﻟﻤﻔﺘﺎح‬ ‫ﻏﻠﻖ‬ ‫ﻟﺤﻈﺔ‬)‫اﻻﻋﻈﻢ‬ ‫ﻣﻘﺪارھﺎ‬ ‫ﻓﻲ‬ ‫وﺗﻜﻮن‬(
t
I
Lind
∆
∆
=ε ‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻗﺎﻧﻮن‬ ‫ﻣﻦ‬
t
N B
ind
∆
∆Φ
=ε ‫ﻓﺮاداي‬ ‫ﻗﺎﻧﻮن‬ ‫ﻣﻦ‬
RIV insappind −=ε ‫اﻟﺤﺜﯿﺔ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻣﻦ‬
appind V%x=ε ‫اﻟﻤﻮﺿﻮﻋﺔ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﻣﻦ‬ ‫ﻣﺌﻮﯾﺔ‬ ‫ﻧﺴﺒﺔ‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫اﻟﻘﻮة‬ ‫ﺗﻌﻄﻰ‬ ‫ﻋﻨﺪﻣﺎ‬
0ind =ε ‫اﻻﻋﻈﻢ‬ ‫ﻣﻘﺪاره‬ ‫اﻟﺘﯿﺎر‬ ‫ﯾﺒﻠﻎ‬ ‫ﻋﻨﺪﻣﺎ‬)‫اﻟﺜﺎﺑﺖ‬(
‫ﻣﻼﺣﻈ‬‫ﺎت‬/
v‫ﻟﻠ‬ ‫ﺔ‬‫اﻟﻤﺌﻮﯾ‬ ‫ﺴﺒﺔ‬‫اﻟﻨ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺔ‬‫اﻟﻤﺤﺘﺜ‬ ‫ﺔ‬‫اﻟﻜﮭﺮﺑﺎﺋﯿ‬ ‫ﺔ‬‫اﻟﺪاﻓﻌ‬ ‫ﻮة‬‫ﻟﻠﻘ‬ ‫ﺔ‬‫اﻟﻤﺌﻮﯾ‬ ‫ﺴﺒﺔ‬‫اﻟﻨ‬ ‫ﺴﺎب‬‫ﺣ‬ ‫ﻦ‬‫ﯾﻤﻜ‬‫ﻮة‬‫ﻟﻠﻘ‬ ‫ﺔ‬‫اﻟﻤﺌﻮﯾ‬ ‫ﺴﺒﺔ‬‫اﻟﻨ‬ ‫ﺚ‬‫ﺣﯿ‬ ‫ﺎر‬‫ﺘﯿ‬
‫ﺗﺴﺎوي‬ ‫اﻟﺤﺎﻟﺔ‬ ‫ھﺬه‬ ‫ﻓﻲ‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬)100%(‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫ﺔ‬‫اﻟﻤﺌﻮﯾ‬ ‫اﻟﻨﺴﺒﺔ‬ ‫ﻣﻨﮭﺎ‬ ‫ﻣﻄﺮوح‬.‫ﺴﺎب‬‫ﺣ‬ ‫ﻦ‬‫ﯾﻤﻜ‬ ‫ﺬﻟﻚ‬‫ﻛ‬
‫ﺔ‬‫اﻟﺤﺎﻟ‬ ‫ﺬه‬‫ھ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫ﺔ‬‫اﻟﻤﺌﻮﯾ‬ ‫ﺴﺒﺔ‬‫اﻟﻨ‬ ‫ﺚ‬‫ﺣﯿ‬ ‫ﺔ‬‫اﻟﻤﺤﺘﺜ‬ ‫ﺔ‬‫اﻟﻜﮭﺮﺑﺎﺋﯿ‬ ‫ﺔ‬‫اﻟﺪاﻓﻌ‬ ‫ﻮة‬‫ﻟﻠﻘ‬ ‫ﺔ‬‫اﻟﻤﺌﻮﯾ‬ ‫اﻟﻨﺴﺒﺔ‬ ‫ﻣﻦ‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻤﺌﻮﯾﺔ‬ ‫اﻟﻨﺴﺒﺔ‬
‫ﺗﺴﺎوي‬)100%(‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫ﻟﻠﻘﻮة‬ ‫اﻟﻤﺌﻮﯾﺔ‬ ‫اﻟﻨﺴﺒﺔ‬ ‫ﻣﻨﮭﺎ‬ ‫ﻣﻄﺮوح‬.
v‫ﯿﻦ‬‫ﺑ‬ ‫ﺔ‬‫اﻟﻌﻼﻗ‬ ‫ﺎن‬‫ﻓ‬ ‫ﺬﻟﻚ‬‫ﻟ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﻲ‬‫ﻓ‬ ‫اﻟﻤﻨﺴﺎب‬ ‫اﻟﺘﯿﺎر‬ ‫ﻣﻘﺪار‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫ﯾﺘﻨﺎﺳﺐ‬ ‫ﻣﻠﻒ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ان‬
‫اﻟﻔﯿﺾ‬‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬‫ھﻲ‬ ‫واﻟﺘﯿﺎر‬ ‫اﻟﻤﻠﻒ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬:
‫اﻟﻜﻤ‬ ‫ﺗﺴﻤﻰ‬ ‫ﺣﯿﺚ‬‫ﯿﺔ‬)NФB(‫اﻟﻤﻠﻒ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬)‫اﻟﻜﻠﻲ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬(‫ﺑﻮﺣﺪة‬ ‫وﯾﻘﺎس‬)wb(
‫اﻣﺎ‬)ФB(‫ﺑﻮﺣﺪة‬ ‫وﯾﻘﺎس‬ ‫اﻟﻤﻠﻒ‬ ‫ﻟﻔﺎت‬ ‫ﻣﻦ‬ ‫واﺣﺪة‬ ‫ﻟﻔﺔ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬)wb.(
ILN B =Φ
constins I%XI =
R
V
I
app
const =
R
V
I
indapp
ins
ε−
=

28. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-29-
v‫ﻓ‬ ‫ﺴﺎب‬‫اﻟﻤﻨ‬ ‫ﺎر‬‫ﺑﺎﻟﺘﯿ‬ ‫ﺮ‬‫اﻟﺘﻐﯿ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺐ‬‫ﯾﺘﻨﺎﺳ‬ ‫ﻮ‬‫ﻓﮭ‬ ‫اﻟﻤﻠﻒ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫ﺑﺎﻟﻔﯿﺾ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫اﻣﺎ‬‫ﺬﻟﻚ‬‫ﻟ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﻲ‬
‫ﺑﺎﻟﻔﯿﺾ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻓﺎن‬‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬‫ھﻲ‬ ‫اﻟﺘﯿﺎر‬ ‫وﺗﻐﯿﺮ‬ ‫اﻟﻤﻠﻒ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬:
‫و‬‫اﻟﻜﻤﯿﺔ‬ ‫ﺗﺴﻤﻰ‬)NΔФB(‫ﺪة‬‫ﺑﻮﺣ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﺮق‬‫ﯾﺨﺘ‬ ‫ﺬي‬‫اﻟ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫ﺑﺎﻟﻔﯿﺾ‬ ‫ﺑﺎﻟﺘﻐﯿﺮ‬)wb(‫ﺎ‬‫ﺑﯿﻨﻤ‬)ΔФB(‫ﺎﻟﻔﯿﺾ‬‫ﺑ‬ ‫ﺮ‬‫اﻟﺘﻐﯿ‬
‫اﻟ‬‫ﻟﻔﺎت‬ ‫ﻣﻦ‬ ‫ﻟﻔﺔ‬ ‫ﻛﻞ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬ ‫ﻤﻐﻨﺎطﯿﺴﻲ‬‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﻠﻒ‬)wb(
‫ﻟﺬﻟﻚ‬‫ﺪد‬‫ﻋ‬ ‫ﻦ‬‫ﻋ‬ ‫ﻮض‬‫ﻧﻌ‬ ‫ﻻ‬ ‫اﻟﻤﻠﻒ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫ﺑﺎﻟﻔﯿﺾ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫او‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫اﯾﺠﺎد‬ ‫اﻟﻤﻄﻠﻮب‬ ‫ﻛﺎن‬ ‫اذا‬
‫اﻟﻠﻔﺎت‬)N(‫ﻦ‬‫ﻣ‬ ‫ﺪة‬‫واﺣ‬ ‫ﺔ‬‫ﻟﻔ‬ ‫ﺮق‬‫ﯾﺨﺘ‬ ‫اﻟﺬي‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫ﺑﺎﻟﻔﯿﺾ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫او‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫اﯾﺠﺎد‬ ‫اﻟﻤﻄﻠﻮب‬ ‫ﻛﺎن‬ ‫اذا‬ ‫ﺑﯿﻨﻤﺎ‬
‫اﻟﻠ‬ ‫ﻋﺪد‬ ‫ﻋﻦ‬ ‫ﻧﻌﻮض‬ ‫اﻟﻤﻠﻒ‬ ‫ﻟﻔﺎت‬‫ﻔﺎت‬)N.(
‫اﻟﻤﺤﺚ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬:
‫اﻻﺗﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬ ‫ﻟﻠﻤﺤﺚ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻋﻦ‬ ‫ﯾﻌﺒﺮ‬:
‫ﻋﻠﻰ‬ ‫اﻟﻤﺤﺚ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺨﺘﺰﻧﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺗﻌﺘﻤﺪ‬:
1-‫ﻟﻠﻤﺤﺚ‬ ‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬. (2-‫ا‬ ‫اﻟﺘﯿﺎر‬ ‫ﻣﺮﺑﻊ‬‫اﻟﻤﺤﺚ‬ ‫ﻓﻲ‬ ‫ﻟﻤﺎر‬)‫طﺮدي‬ ‫ﺗﻨﺎﺳﺐ‬.(
•‫اﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺗﻘﺎس‬)PE(‫ﺑﺎﻟﺠﻮل‬)J(‫ﺑﺎﻟﮭﻨﺮي‬ ‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫ﯾﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬)H(‫ﺑﺎﻻﻣﺒﯿﺮ‬ ‫واﻟﺘﯿﺎر‬)A. (
•‫اﻟﻄﺎﻗﺔ‬ ‫ﺿﯿﺎع‬ ‫ﻓﻲ‬ ‫ﯾﺘﺴﺒﺐ‬ ‫ﻻ‬ ‫اﻟﻤﺤﺚ‬ ‫ان‬ ‫ﯾﻌﻨﻲ‬ ‫وھﺬا‬ ‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ ‫ﻣﻘﺎوﻣﺘﮫ‬ ‫ان‬ ‫أي‬ ‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﻣﮭﻤﻞ‬ ‫ﻣﻠﻒ‬ ‫اﻟﻤﺤﺚ‬ ‫ﯾﻌﺘﺒﺮ‬.
‫اﻟﻤﺘﺒﺎدل‬ ‫اﻟﺤﺚ‬ ‫ﻇﺎﻫﺮة‬:‫ظﺎ‬ ‫ھﻲ‬‫اﻟﺜﺎﻧﻮي‬ ‫اﻟﻤﻠﻒ‬ ‫ﻓﻲ‬ ‫ﻣﺤﺘﺜﺔ‬ ‫ﻛﮭﺮﺑﺎﺋﯿﺔ‬ ‫داﻓﻌﺔ‬ ‫ﻗﻮة‬ ‫ﺗﻮﻟﯿﺪ‬ ‫ھﺮة‬)εind(2)(‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﺎر‬‫ﺗﯿ‬ ‫ﺮ‬‫ﻟﺘﻐﯿ‬ ‫ﻧﺘﯿﺠﺔ‬
‫اﻟﺰﻣﻦ‬ ‫ﻟﻮﺣﺪة‬ ‫اﻻﺑﺘﺪاﺋﻲ‬.
♦‫ﻓ‬‫ﺔ‬‫زﻣﻨﯿ‬ ‫ﺮة‬‫ﻓﺘ‬ ‫ﻼل‬‫ﺧ‬ ‫ﺼﻔﺮ‬‫اﻟ‬ ‫ﻰ‬‫اﻟ‬ ‫ﺔ‬‫اﻟﺜﺎﺑﺘ‬ ‫ﮫ‬‫ﻗﯿﻤﺘ‬ ‫ﻦ‬‫ﻣ‬ ‫ﯾﺘﻼﺷﻰ‬ ‫او‬ ‫اﻟﺜﺎﺑﺘﺔ‬ ‫ﻗﯿﻤﺘﮫ‬ ‫اﻟﻰ‬ ‫اﻟﺼﻔﺮ‬ ‫ﻣﻦ‬ ‫اﻟﺘﯿﺎر‬ ‫ﯾﻨﻤﻮ‬ ‫ﻌﻨﺪﻣﺎ‬‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫ﻣﻌﯿﻨ‬
‫اﻟﺬاﺗ‬ ‫اﻟﺤﺚ‬ ‫ﻟﻈﺎھﺮة‬ ‫ووﻓﻘﺎ‬ ‫اﻻﺑﺘﺪاﺋﻲ‬ ‫اﻟﻤﻠﻒ‬‫ﺔ‬‫ذاﺗﯿ‬ ‫ﺔ‬‫ﻣﺤﺘﺜ‬ ‫ﺔ‬‫ﻛﮭﺮﺑﺎﺋﯿ‬ ‫ﺔ‬‫داﻓﻌ‬ ‫ﻗﻮة‬ ‫اﻟﻤﻠﻒ‬ ‫طﺮﻓﻲ‬ ‫ﻋﻠﻰ‬ ‫ﺗﺘﻮﻟﺪ‬ ‫ﺳﻮف‬ ‫ﻲ‬)εind1(
‫ﻣﺤﺘﺜﺔ‬ ‫ﻛﮭﺮﺑﺎﺋﯿﺔ‬ ‫داﻓﻌﺔ‬ ‫ﻗﻮة‬ ‫ﺗﻮﻟﯿﺪه‬ ‫ﻋﻦ‬ ‫ﻓﻀﻼ‬)εind2(‫ﻟﮫ‬ ‫ﻣﺠﺎور‬ ‫اﺧﺮ‬ ‫ﻣﻠﻒ‬ ‫ﻓﻲ‬‫ﺎﻧﻮي‬‫اﻟﺜ‬ ‫ﺑﺎﻟﻤﻠﻒ‬ ‫ﯾﺴﻤﻰ‬ ‫ﺑﮫ‬ ‫ﻣﺤﯿﻂ‬ ‫او‬‫ﺎ‬‫وﻓﻘ‬
‫ﻲ‬ ‫ﻓ‬ ‫ﺔ‬‫اﻟﻤﺤﺘﺜ‬ ‫ﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿ‬ ‫ﺔ‬‫اﻟﺪاﻓﻌ‬ ‫ﻮة‬ ‫اﻟﻘ‬ ‫ﺬه‬‫ھ‬ ‫ﺪار‬ ‫ﻣﻘ‬ ‫وان‬ ‫ﺎدل‬‫اﻟﻤﺘﺒ‬ ‫ﺚ‬‫اﻟﺤ‬ ‫ﺎھﺮة‬‫ظ‬ ‫ﺴﻤﻰ‬ ‫ﺗ‬ ‫ﺮى‬‫اﺧ‬ ‫ﺎھﺮة‬‫ﻟﻈ‬‫ﺎﻧﻮي‬‫اﻟﺜ‬ ‫ﻒ‬‫اﻟﻤﻠ‬
‫ﯾﺘﻨﺎﺳ‬‫ﺐ‬‫اﻻﺑﺘﺪاﺋﻲ‬ ‫اﻟﻤﻠﻒ‬ ‫ﻓﻲ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻟﺘﻐﯿﺮ‬ ‫اﻟﺰﻣﻨﻲ‬ ‫اﻟﻤﻌﺪل‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬.
‫اﻟﺜﺎﻧﻮي‬ ‫اﻟﻤﻠﻒ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﻬﺮﺑﺎﺋﻴﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫اﻟﻘﻮة‬ ‫ﺣﺴﺎب‬:
‫ﺴﺒﺐ‬‫اﻟﻤ‬ ‫ﺎﻛﺲ‬‫ﺗﻌ‬ ‫ﺎﻧﻮي‬‫اﻟﺜ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫ﻣﺤﺘﺜ‬ ‫ﻛﮭﺮﺑﺎﺋﯿﺔ‬ ‫داﻓﻌﺔ‬ ‫ﻗﻮة‬ ‫ﺗﺘﻮﻟﺪ‬ ‫اﻟﺰﻣﻦ‬ ‫ﻟﻮﺣﺪة‬ ‫اﻻﺑﺘﺪاﺋﻲ‬ ‫اﻟﻤﻠﻒ‬ ‫ﻓﻲ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻟﺘﻐﯿﺮ‬ ‫ﻧﺘﯿﺠﺔ‬
‫وﻟﺪھﺎ‬ ‫اﻟﺬي‬‫ﻟﻨﺰ‬ ‫ﻟﻘﺎﻧﻮن‬ ‫طﺒﻘﺎ‬)‫ﺑﺎﻟﺘﯿﺎر‬ ‫اﻟﺘﻐﯿﺮ‬ ‫ﺗﻌﺎﻛﺲ‬ ‫أي‬‫ﺪاﺋﻲ‬‫اﻻﺑﺘ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﻲ‬‫ﻓ‬ ‫اﻟﻤﺎر‬‫ﺰﻣﻦ‬‫اﻟ‬ ‫ﺪة‬‫ﻟﻮﺣ‬(‫ﺔ‬‫اﻟﺪاﻓﻌ‬ ‫ﻮة‬‫اﻟﻘ‬ ‫ﺴﺐ‬‫وﺗﺤ‬ ،
‫اﻟﺘﺎﻟﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬ ‫اﻟﺜﺎﻧﻮي‬ ‫اﻟﻤﻠﻒ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬:
‫ﺣﯿﺚ‬:
εind2:‫ﺼﻔﺮ‬‫اﻟ‬ ‫ﻣﻦ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻧﻤﻮ‬ ‫ﻋﻨﺪ‬ ‫ﺳﺎﻟﺒﺔ‬ ‫وﺗﻜﻮن‬ ‫ﻓﻮﻟﻂ‬ ‫ﺑﻮﺣﺪة‬ ‫اﻟﺜﺎﻧﻮي‬ ‫اﻟﻤﻠﻒ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺘﻮﻟﺪة‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫اﻟﻘﻮة‬
‫ﺪھﺎ‬‫وﻟ‬ ‫ﺬي‬‫اﻟ‬ ‫ﺴﺒﺐ‬‫اﻟﻤ‬ ‫ﺎﻛﺲ‬‫ﺗﻌ‬ ‫ﺎ‬‫ﻻﻧﮭ‬ ‫ﺼﻔﺮ‬‫اﻟ‬ ‫ﻰ‬‫اﻟ‬ ‫ﻢ‬‫اﻻﻋﻈ‬ ‫ﺪار‬‫اﻟﻤﻘ‬ ‫ﻣﻦ‬ ‫اﻟﺘﯿﺎر‬ ‫ﺗﻼﺷﻲ‬ ‫ﻋﻨﺪ‬ ‫ﻣﻮﺟﺒﺔ‬ ‫وﺗﻜﻮن‬ ‫اﻻﻋﻈﻢ‬ ‫اﻟﻤﻘﺪار‬ ‫اﻟﻰ‬
‫ﻟﻨﺰ‬ ‫ﻟﻘﺎﻧﻮن‬ ‫طﺒﻘﺎ‬.
ILN B ∆=∆Φ
121 III −=∆
t
I
M 1
)2(ind
∆
∆
−=ε
2
IL
2
1
PE =
‫اﻟ‬ ‫اﻟﺤﺚ‬ ‫ﻗﺎﻧﻮن‬‫ﻤﺘﺒﺎدل‬

29. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-30-
M:‫اﻟﻤﺘﺒﺎدل‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬‫ﺬاﺗﻲ‬‫اﻟ‬ ‫ﺚ‬‫اﻟﺤ‬ ‫ﻞ‬‫ﻣﻌﺎﻣ‬ ‫وﺣﺪة‬ ‫ﻧﻔﺲ‬ ‫ھﻲ‬ ‫ووﺣﺪﺗﮫ‬ ‫اﻟﻤﻠﻔﯿﻦ‬ ‫ﺑﯿﻦ‬)L(‫ﺮي‬‫اﻟﮭﻨ‬ ‫ﻲ‬‫وھ‬)H(‫ﺪار‬‫ﻣﻘ‬ ‫ﻮ‬‫وھ‬
‫داﺋﻤﺎ‬ ‫ﻣﻮﺟﺐ‬.‫ﺑﺎﻧﮫ‬ ‫ﻣﻠﻔﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺘﺒﺎدل‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫وﯾﻌﺮف‬)‫ﻧﺴﺒﺔ‬‫ﺪل‬‫اﻟﻤﻌ‬ ‫ﻰ‬‫إﻟ‬ ‫ﻒ‬‫ﻣﻠ‬ ‫ﻲ‬‫ﻓ‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫اﻟﻘﻮة‬
‫ﺑﮫ‬ ‫ﻣﺤﯿﻂ‬ ‫او‬ ‫ﻟﮫ‬ ‫ﻣﺠﺎور‬ ‫اﺧﺮ‬ ‫ﻣﻠﻒ‬ ‫ﻓﻲ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻟﺘﻐﯿﺮ‬ ‫اﻟﺰﻣﻨﻲ‬. (
‫ﺑﻤﻮﺟﺐ‬ ‫ﻟﺬﻟﻚ‬‫اﻵﺗﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬ ‫ﯾﺤﺴﺐ‬ ‫اﻟﻤﻠﻔﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺘﺒﺎدل‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫ﻓﺎن‬ ‫اﻟﺘﻌﺮﯾﻒ‬ ‫ھﺬا‬:
‫اﻟﻤﺘﺒﺎدل‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫وﯾﻘﺎس‬)M(‫اﻟﮭﻨﺮي‬ ‫وھﻲ‬ ‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫وﺣﺪة‬ ‫ﺑﻨﻔﺲ‬)H(‫اﺟﺰاءه‬ ‫او‬)mH or μH. (
t
I1
∆
∆
:‫ﺎر‬ ‫اﻟﺘﯿ‬ ‫ﺮ‬ ‫ﻟﺘﻐﯿ‬ ‫ﻲ‬ ‫اﻟﺰﻣﻨ‬ ‫ﺪل‬ ‫اﻟﻤﻌ‬‫ﺪة‬ ‫ﺑﻮﺣ‬ ‫ﺪاﺋﻲ‬ ‫اﻻﺑﺘ‬ ‫ﻒ‬ ‫اﻟﻤﻠ‬ ‫ﻲ‬ ‫ﻓ‬)A/s(‫ﺬاﺗﻲ‬ ‫اﻟ‬ ‫ﺚ‬ ‫اﻟﺤ‬ ‫ﺎﻧﻮن‬ ‫ﻗ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﺴﺐ‬ ‫ﯾﺤ‬ ‫ان‬ ‫ﻦ‬ ‫وﯾﻤﻜ‬
)‫ﺑﻤﻌﺮﻓﺔ‬1indε(‫اﻻﻧﻲ‬ ‫اﻟﺘﯿﺎر‬ ‫ﺑﻤﻌﺮﻓﺔ‬ ‫اﻟﺤﺜﯿﺔ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻣﻦ‬ ‫او‬)Iins(‫اﻟﻤﻮﺿﻮﻋﺔ‬ ‫واﻟﻔﻮﻟﻄﯿﺔ‬)Vapp(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬:
t
I
LRIVor
t
I
L 1
11insapp
1
11ind
∆
∆
+=
∆
∆
=ε
ΔI1:‫اﻻﺑﺘﺪاﺋﻲ‬ ‫اﻟﻤﻠﻒ‬ ‫ﺗﯿﺎر‬ ‫ﺗﻐﯿﺮ‬‫ﺣﯿﺚ‬)ΔI1=I2 – I1(‫و‬‫ﯾﻜﻮن‬‫اﻟﺘﻐﯿﺮ‬ ‫ھﺬا‬‫ﻻن‬ ‫ﺎر‬‫اﻟﺘﯿ‬ ‫ﻧﻤﻮ‬ ‫ﻋﻨﺪ‬ ‫ﻣﻮﺟﺐ‬)I2 > I1(‫ﻮن‬‫وﯾﻜ‬
‫ﻻن‬ ‫اﻟﺘﯿﺎر‬ ‫ﺗﻼﺷﻲ‬ ‫ﻋﻨﺪ‬ ‫ﺳﺎﻟﺐ‬)12 < 11.(
‫اﻹﺷﺎرة‬‫اﻟﺴﺎﻟﺒﺔ‬‫اﻟﻘﺎﻧﻮن‬ ‫ﻓﻲ‬‫اﻟﻤﻠﻒ‬ ‫ﺗﯿﺎر‬ ‫ﻓﻲ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫ﺗﻌﺎﻛﺲ‬ ‫اﻟﺜﺎﻧﻮي‬ ‫اﻟﻤﻠﻒ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺤﺘﺜﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫اﻟﺪاﻓﻌﺔ‬ ‫اﻟﻘﻮة‬ ‫ان‬ ‫ﺗﻌﻨﻲ‬
‫اﻻﺑﺘﺪاﺋﻲ‬‫ﺣﺜﮭﺎ‬ ‫ﺳﺒﺐ‬ ‫اﻟﺬي‬‫ﻟﻨﺰ‬ ‫ﻗﺎﻧﻮن‬ ‫ﺣﺴﺐ‬.
♦‫وﻋﻠﻰ‬‫ﻲ‬‫ﻓ‬ ‫ﺪة‬‫اﻟﻤﺘﻮﻟ‬ ‫ﺔ‬‫اﻟﻤﺤﺘﺜ‬ ‫ﺔ‬‫اﻟﻜﮭﺮﺑﺎﺋﯿ‬ ‫ﺔ‬‫اﻟﺪاﻓﻌ‬ ‫ﻮة‬‫اﻟﻘ‬ ‫ﺴﺎب‬‫ﺣ‬ ‫ﻦ‬‫ﯾﻤﻜ‬ ‫ﺴﻲ‬‫اﻟﻜﮭﺮوﻣﻐﻨﺎطﯿ‬ ‫ﺚ‬‫اﻟﺤ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺮاداي‬‫ﻓ‬ ‫ﺎﻧﻮن‬‫ﻗ‬ ‫وﻓﻖ‬
‫اﻟﺜﺎﻧﻮي‬ ‫اﻟﻤﻠﻒ‬‫ﻟﻔﺎﺗﮫ‬ ‫ﻋﺪد‬ ‫واﻟﺬي‬)N2(‫اﻵﺗﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬:
‫ا‬ ‫اﻟﻤﻠﻒ‬ ‫ﻳﻜﻮن‬ ‫وﻋﻨﺪﻣﺎ‬‫ﺧﺎرﺟﻴﺔ‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫إﻟﻰ‬ ‫ﻣﺮﺑﻮط‬ ‫ﻟﺜﺎﻧﻮي‬‫اﻟﻜﻠـﻲ‬ ‫ﻣﻘﺪارﻫﺎ‬)R(‫وﻓﻘـﺎ‬ ‫ﻳﺤـﺴﺐ‬ ‫ﻓﻴـﻪ‬ ‫اﻧـﻲ‬ ‫ﻣﺤﺘـﺚ‬ ‫ﺗﻴـﺎر‬ ‫ﻳﺘﻮﻟـﺪ‬
‫ﻳﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اوم‬ ‫ﻟﻘﺎﻧﻮن‬:
‫ﻣﻼﺣﻈ‬‫ﺎت‬/
v‫ﺎم‬ ‫ﺗ‬ ‫ﺴﻲ‬ ‫ﻣﻐﻨﺎطﯿ‬ ‫ﺮان‬ ‫اﻗﺘ‬ ‫ﺎ‬ ‫ﺑﯿﻨﮭﻤ‬ ‫ﺼﻞ‬ ‫ﯾﺤ‬ ‫ﯿﻦ‬ ‫اﻟﻤﻠﻔ‬ ‫ﯿﻦ‬ ‫ﺑ‬ ‫ﻖ‬ ‫ﻣﻐﻠ‬ ‫ﺎوع‬ ‫اﻟﻤﻄ‬ ‫ﺪ‬ ‫اﻟﺤﺪﯾ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﺐ‬ ‫ﻗﻠ‬ ‫ﻮد‬ ‫وﺟ‬ ‫ﺔ‬ ‫ﺣﺎﻟ‬ ‫ﻲ‬ ‫ﻓ‬
)‫ﺗﺎم‬ ‫ﻣﻐﻨﺎطﯿﺴﻲ‬ ‫ﺗﺮاﺑﻂ‬ ‫او‬(‫اﻟﻤﺘﺒﺎ‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬‫ﯿﻦ‬‫اﻟﻤﻠﻔ‬ ‫ﺖ‬‫ﺛﻮاﺑ‬ ‫ﻋﻠﻰ‬ ‫ﻓﻘﻂ‬ ‫ﯾﻌﺘﻤﺪ‬ ‫ﺑﯿﻨﮭﻤﺎ‬ ‫دل‬)L1 , L2(‫ﺴﺐ‬‫وﯾﺤ‬
‫اﻵﺗﯿﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬:
21 LLM ×=
t
I
M
1
2ind
∆
∆
ε
−=
2
2ind
2
R
I
ε
=
t
N 2B
2)2(ind
∆
∆Φ
−=ε ‫اﻟ‬ ‫ﻓﻲ‬ ‫ﻓﺮاداي‬ ‫ﻗﺎﻧﻮن‬ ‫ﺣﺴﺐ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬
‫ا‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫ﺣﺴﺎب‬‫ﻟﻤﺘﺒﺎدل‬‫ﺑ‬‫ﺗﻌﺮﻳﻔﻪ‬ ‫ﻤﻮﺟﺐ‬

30. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-31-
v‫ﺪاﺋﻲ‬‫اﻻﺑﺘ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺴﺎب‬‫اﻟﻤﻨ‬ ‫ﺎر‬‫اﻟﺘﯿ‬ ‫ﺪار‬‫ﻣﻘ‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺐ‬‫ﯾﺘﻨﺎﺳ‬ ‫ﺎﻧﻮي‬‫اﻟﺜ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﺮق‬‫ﯾﺨﺘ‬ ‫ﺬي‬‫اﻟ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ان‬
‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬‫ھﻲ‬ ‫اﻻﺑﺘﺪاﺋﻲ‬ ‫اﻟﻤﻠﻒ‬ ‫وﺗﯿﺎر‬ ‫اﻟﺜﺎﻧﻮي‬ ‫اﻟﻤﻠﻒ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬:
‫ﺔ‬ ‫اﻟﻜﻤﯿ‬ ‫ﺴﻤﻰ‬ ‫ﺗ‬ ‫ﺚ‬‫ﺣﯿ‬)N2ФB2(‫ﺎﻧﻮي‬‫اﻟﺜ‬ ‫ﻒ‬ ‫اﻟﻤﻠ‬ ‫ﺮق‬‫ﯾﺨﺘ‬ ‫ﺬي‬ ‫اﻟ‬ ‫ﺴﻲ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﯿﺾ‬ ‫اﻟﻔ‬)‫ﻲ‬ ‫اﻟﻜﻠ‬ ‫ﺴﻲ‬ ‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﯿﺾ‬ ‫اﻟﻔ‬(‫ﺎس‬ ‫وﯾﻘ‬
‫ﺑﻮﺣﺪة‬)wb(
‫اﻣﺎ‬)ФB2(‫اﻟﺜ‬ ‫اﻟﻤﻠﻒ‬ ‫ﻟﻔﺎت‬ ‫ﻣﻦ‬ ‫واﺣﺪة‬ ‫ﻟﻔﺔ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬‫ﺑﻮﺣﺪة‬ ‫وﯾﻘﺎس‬ ‫ﺎﻧﻮي‬)wb.(
v‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺴﺎب‬‫اﻟﻤﻨ‬ ‫ﺑﺎﻟﺘﯿﺎر‬ ‫اﻟﺘﻐﯿﺮ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫ﯾﺘﻨﺎﺳﺐ‬ ‫ﻓﮭﻮ‬ ‫اﻟﺜﺎﻧﻮي‬ ‫اﻟﻤﻠﻒ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫ﺑﺎﻟﻔﯿﺾ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫اﻣﺎ‬
‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺎر‬‫اﻟﺘﯿ‬ ‫ﺮ‬‫وﺗﻐﯿ‬ ‫ﺎﻧﻮي‬‫اﻟﺜ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﺮق‬‫ﯾﺨﺘ‬ ‫ﺬي‬‫اﻟ‬ ‫ﺴﻲ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﺎﻟﻔﯿﺾ‬‫ﺑ‬ ‫ﺮ‬‫اﻟﺘﻐﯿ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺔ‬‫اﻟﻌﻼﻗ‬ ‫ﺎن‬‫ﻓ‬ ‫ﺬﻟﻚ‬‫ﻟ‬ ‫ﺪاﺋﻲ‬‫اﻻﺑﺘ‬
‫ھﻲ‬ ‫اﻻﺑﺘﺪاﺋﻲ‬:
‫اﻟﻜﻤﯿﺔ‬ ‫ﺗﺴﻤﻰ‬ ‫ﺣﯿﺚ‬)N2ΔФB2(‫ﺪة‬‫ﺑﻮﺣ‬ ‫ﺎﻧﻮي‬‫اﻟﺜ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﺮق‬‫ﯾﺨﺘ‬ ‫ﺬي‬‫اﻟ‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫ﺑﺎﻟﻔﯿﺾ‬ ‫ﺑﺎﻟﺘﻐﯿﺮ‬)wb(‫ﺎ‬‫ﺑﯿﻨﻤ‬)ΔФB2(
‫ﺑﻮﺣﺪة‬ ‫اﻟﺜﺎﻧﻮي‬ ‫اﻟﻤﻠﻒ‬ ‫ﻟﻔﺎت‬ ‫ﻣﻦ‬ ‫ﻟﻔﺔ‬ ‫ﻛﻞ‬ ‫ﯾﺨﺘﺮق‬ ‫اﻟﺬي‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫ﺑﺎﻟﻔﯿﺾ‬ ‫اﻟﺘﻐﯿﺮ‬)wb(
‫ﺑﺎﻟﻔﯿ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫او‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫اﯾﺠﺎد‬ ‫اﻟﻤﻄﻠﻮب‬ ‫ﻛﺎن‬ ‫اذا‬ ‫ﻟﺬﻟﻚ‬‫ﻮض‬‫ﻧﻌ‬ ‫ﻻ‬ ‫ﺎﻧﻮي‬‫اﻟﺜ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﺮق‬‫ﯾﺨﺘ‬ ‫ﺬي‬‫اﻟ‬ ‫ﺴﻲ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﺾ‬
‫اﻟﻠﻔﺎت‬ ‫ﻋﺪد‬ ‫ﻋﻦ‬)N2(‫ﺔ‬‫ﻟﻔ‬ ‫ﺮق‬‫ﯾﺨﺘ‬ ‫ﺬي‬‫اﻟ‬ ‫ﺴﻲ‬‫اﻟﻤﻐﻨﺎطﯿ‬ ‫ﺎﻟﻔﯿﺾ‬‫ﺑ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫او‬ ‫اﻟﻤﻐﻨﺎطﯿﺴﻲ‬ ‫اﻟﻔﯿﺾ‬ ‫اﯾﺠﺎد‬ ‫اﻟﻤﻄﻠﻮب‬ ‫ﻛﺎن‬ ‫اذا‬ ‫ﺑﯿﻨﻤﺎ‬
‫اﻟﻤﻠﻒ‬ ‫ﻟﻔﺎت‬ ‫ﻣﻦ‬ ‫واﺣﺪة‬‫اﻟﺜﺎﻧﻮي‬‫اﻟﻠﻔﺎت‬ ‫ﻋﺪد‬ ‫ﻋﻦ‬ ‫ﻧﻌﻮض‬)N2.(
‫اﻟﺜﺎﻧﻲ‬ ‫اﻟﻔﺼﻞ‬ ‫ﻗﻮاﻧﻴﻦ‬)‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫اﻟﺤﺚ‬(
‫اﻟ‬ ‫اﻟﻘﻮة‬‫اﻟﻤﻐﻨﺎﻃﻴﺴﻴﺔ‬ ‫واﻟﻘﻮة‬ ‫ﻜﻬﺮﺑﺎﺋﻴﺔ‬:
θν== sinBqF,EqF BE
‫اﻟﻤﻮﺻﻠﺔ‬ ‫اﻟﺴﺎق‬ ‫ﻗﻮاﻧﻴﻦ‬:
R
PorIPorRIP
BIF,BIF,
t
q
I,
R
I
sinB
2
motional
dissipatedmotionaldissipated
2
dissipated
pull2B
motional
ind
motional
ε
=ε==
==
∆
=
ε
=
θν=ε
ll
l
‫اﻟﻤﻐﻨﺎﻃﻴﺴﻲ‬ ‫اﻟﻔﻴﺾ‬ ‫ﺑﻜﺜﺎﻓﺔ‬ ‫اﻟﻤﻐﻨﺎﻃﻴﺴﻲ‬ ‫اﻟﻔﻴﺾ‬ ‫ﻋﻼﻗﺔ‬:
)cosAB(,cosAB BB θ∆=∆Φθ=Φ
‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻗﻮاﻧﻴﻦ‬)‫ﻓﺮاداي‬ ‫ﻗﻮاﻧﻴﻦ‬(:
1212121B2BB
indind
indind
B
ind
coscoscos,AAA,BBB,
t
q
I,RIor
t
cos
NABor
cos
t
A
NBorcos
t
B
NAor
t
N
θ−θ=θ∆−=∆−=∆Φ−Φ=∆Φ
∆
∆
==ε
∆
θ∆
−=ε
θ
∆
∆
−=εθ
∆
∆
−=ε
∆
∆Φ
−=ε
12B2 IMN ∆=∆Φ
12B2 IMN =Φ

31. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻧﻲ‬:‫اﻟ‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫ﺤﺚ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-32-
‫اﻟﻤﻮﻟﺪ‬ ‫ﻗﻮاﻧﻴﻦ‬)‫ﻣﻌﺎدﻻ‬‫ت‬‫واﻟﺘﻴﺎر‬ ‫اﻟﻔﻮﻟﻄﻴﺔ‬:(
R
PorRIPorIP
R
PorRIPorIP
R
I,
R
I
f2,BNA,
)tsin(II
)tsin(
2
max
max
2
maxmaxmaxmaxmax
2
ins
ins
2
insinsinsinsins
max
max
ins
ins
max
maxins
maxins
ε
==ε=
ε
==ε=
ε
=
ε
=
π=ωω=ε


ω=
ωε=ε
‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻗﻮاﻧﻴﻦ‬:
R
V
I,I%xI,V%xorRIV
t
NRIVor
t
I
LRIVorRIV
IL
2
1
PE,ILNorILN
,III
t
Nor
t
I
L
app
constconstinsappindinsappind
B
insappinsappindinsapp
2
BB
1B2BB12
B
indind
===ε−=ε
∆
∆Φ
+=
∆
∆
+=ε+=
==Φ∆=∆Φ
Φ−Φ=∆Φ−=∆
∆
∆Φ
−=ε
∆
∆
−=ε
,
‫اﻟﻤﺘﺒﺎدل‬ ‫اﻟﺤﺚ‬ ‫ﻗﻮاﻧﻴﻦ‬:
1insapp1ind
1
1ind1
2112B212B2
1B2B2B121
222ind
2B
22ind
1
2ind
RIV,
Lt
I
LLM,IMNorIMN
,III
RIor
t
Nor
t
I
M
−=ε
ε
−=
∆
∆
==Φ∆=∆Φ
Φ−Φ=∆Φ−=∆
=ε
∆
∆Φ
−=ε
∆
∆
−=ε

32. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-33-
‫ﺻﺮف‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﻓﻴﻬﺎ‬ ‫اﻟﺤﻤﻞ‬ ‫ﻣﺘﻨﺎوب‬ ‫ﺗﻴﺎر‬ ‫داﺋﺮة‬:
v‫ﻣﺘﻄﺎﺑﻘـﺎن‬ ‫ﻟﻠﺘﻴﺎر‬ ‫اﻟﻄﻮر‬ ‫وﻣﺘﺠﻪ‬ ‫ﻟﻠﻔﻮﻟﻄﻴﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﻪ‬ ‫ﻳﻜﻮن‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻫﺬه‬ ‫ﻓﻲ‬)‫ﻣﺘﻼزﻣـﺎن‬(‫زاوﻳـﺔ‬ ‫ﺑﻴﻨﻬﻤـﺎ‬ ‫ﺗﻮﺟـﺪ‬ ‫ﻻ‬ ‫أي‬
‫ﻃﻮر‬ ‫ﻓﺮق‬)φ(‫ان‬ ‫أي‬) :0=φ(‫ﻟﻠﺘﻴﺎر‬ ‫اﻟﻄﻮر‬ ‫وﻣﺘﺠﻪ‬ ‫ﻟﻠﻔﻮﻟﻄﻴﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﻪ‬ ‫ﺑﻴﻦ‬.
v‫اﻟ‬‫اﻟﻄﻮر‬ ‫ﻤﻌﺎدﻻت‬‫ﻳﺔ‬)‫اﻻﻧﻴﺔ‬(‫اﻻﺗﻴﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺎت‬ ‫ﻋﻨﻬﺎ‬ ‫ﻳﻌﺒﺮ‬ ‫واﻟﺘﻴﺎر‬ ‫ﻟﻠﻔﻮﻟﻄﻴﺔ‬:
‫ﺣﯿﺚ‬:
VR:‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﻋﺒﺮ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻵﻧﻲ‬ ‫اﻟﻤﻘﺪار‬R.
Vm:‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﻋﺒﺮ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻷﻋﻈﻢ‬ ‫اﻟﻤﻘﺪار‬R.
IR:‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﻓﻲ‬ ‫اﻟﻤﻨﺴﺎب‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻵﻧﻲ‬ ‫اﻟﻤﻘﺪار‬R.
Im:‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﻓﻲ‬ ‫اﻟﻤﻨﺴﺎب‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻷﻋﻈﻢ‬ ‫اﻟﻤﻘﺪار‬R.
ωt:‫ـ‬‫ﺑ‬ ‫ﺎس‬‫وﺗﻘ‬ ‫ﻮري‬‫اﻟﻄ‬ ‫ﮫ‬‫ﻟﻠﻤﺘﺠ‬ ‫اﻟﻄﻮر‬ ‫زاوﯾﺔ‬)rad) (‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫او‬ ‫ﺔ‬‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺼﻮرة‬‫اﻟﻤﺤ‬ ‫ﺔ‬‫اﻟﺰاوﯾ‬
‫واﻟﻤﺤﻮر‬ ‫ﻟﻠﺘﯿﺎر‬X. (
v‫ﺑﺎﻟﻌ‬ ‫ﻋﻨﻬﺎ‬ ‫ﻳﻌﺒﺮ‬ ‫اﻟﻔﻌﺎﻟﺔ‬ ‫او‬ ‫اﻟﻤﺆﺛﺮة‬ ‫ﺑﻘﻴﻤﻬﻢ‬ ‫اﻟﻌﻈﻤﻰ‬ ‫اﻟﻔﻮﻟﻄﻴﺔ‬ ‫او‬ ‫اﻻﻋﻈﻢ‬ ‫اﻟﺘﻴﺎر‬ ‫ﺑﻴﻦ‬ ‫اﻟﻌﻼﻗﺔ‬‫اﻻﺗﻴﺔ‬ ‫اﻟﺮﻳﺎﺿﻴﺔ‬ ‫ﻼﻗﺎت‬:
‫ﻢ‬ ‫أﻋﻈ‬ ‫ﺪار‬ ‫ﻣﻘ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﻞ‬ ‫اﻟﺘﺤﻮﯾ‬
‫ﻣﺆﺛﺮ‬ ‫ﻣﻘﺪار‬ ‫إﻟﻰ‬ ‫ﻟﻠﺘﯿﺎر‬
‫ﺆﺛﺮ‬ ‫ﻣ‬ ‫ﺪار‬ ‫ﻣﻘ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﻞ‬ ‫اﻟﺘﺤﻮﯾ‬
‫أﻋﻈﻢ‬ ‫ﻣﻘﺪار‬ ‫إﻟﻰ‬ ‫ﻟﻠﺘﯿﺎر‬
‫ﻢ‬ ‫أﻋﻈ‬ ‫ﺪار‬ ‫ﻣﻘ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﻞ‬ ‫اﻟﺘﺤﻮﯾ‬
‫ﻣﺆﺛﺮ‬ ‫ﻣﻘﺪار‬ ‫إﻟﻰ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬
‫ﺆﺛﺮ‬ ‫ﻣ‬ ‫ﺪار‬ ‫ﻣﻘ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﻞ‬ ‫اﻟﺘﺤﻮﯾ‬
‫أﻋﻈﻢ‬ ‫ﻣﻘﺪار‬ ‫إﻟﻰ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬
2
I
I m
eff = or
Ieff =0.707 Im
Im = 2 Ieff or
Im = 1.414 Ieff 2
V
V m
eff = or
Veff =0.707 Vm
Vm = 2 Veff or
Vm = 1.414 Veff
‫اﻟﺤﺎﺟﺔ‬ ‫ﻋﻨﺪ‬ ‫اﺳﺘﻔﺪ‬:
07.725,656.524,242.423,828.222,414.12 =====
v‫ﻳﻠﻲ‬ ‫ﻛﻤﺎ‬ ‫ﺻﺮف‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺗﺤﺘﻮي‬ ‫ﻟﺪاﺋﺮة‬ ‫اوم‬ ‫ﻗﺎﻧﻮن‬ ‫ﻋﻦ‬ ‫ﻳﻌﺒﺮ‬:
‫س‬/‫ﯾﺴﺎوي‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻤﺆﺛﺮ‬ ‫اﻟﻤﻘﺪار‬ ‫ان‬ ‫اﺛﺒﺖ‬0.707‫؟‬ ‫اﻷﻋﻈﻢ‬ ‫ﻣﻘﺪاره‬ ‫ﻣﻦ‬
‫ج‬/
meff
m
eff
2
m
eff
2
m2
eff
2
m
2
eff
222
m
2
eff
2
m
2
eff
maceffdc
2
ac
2
dc
2
ac
2
dcacdc
I707.0I
2
I
I
2
I
I
2
I
II
2
1
I
2
1
)t(sin,)t(sinII)tsinI(I
)tsin(II,II
IIRIRIPP
=∴
=⇒=⇒=⇒=∴
=ωω=⇒ω=∴
ω==
=⇒=⇒=
Q
Q
)tsin(II
)tsin(VV
mR
mR
ω=
ω= ‫اﻟ‬ ‫ﻫﺬه‬‫اﻻﻧﻴﺔ‬ ‫اﻟﻘﻴﻢ‬ ‫ﺑﻴﻦ‬ ‫ﻋﻼﻗﺔ‬ ‫ﺗﻤﺜﻞ‬ ‫ﻤﻌﺎدﻻت‬
‫واﻟﻔﻮﻟﻄﻴﺔ‬ ‫اﻟﺘﻴﺎر‬ ‫ﻣﻦ‬ ‫ﻟﻜﻞ‬ ‫اﻟﻌﻈﻤﻰ‬ ‫واﻟﻘﻴﻢ‬
eff
eff
m
m
R
R
I
V
Ror
I
V
Ror
I
V
R ===

33. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-34-
v‫ﺻﺮف‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺗﺤﺘﻮي‬ ‫ﻣﺘﻨﺎوب‬ ‫ﺗﻴﺎر‬ ‫داﺋﺮة‬ ‫ﻓﻲ‬ ‫اﻟﻘﺪرة‬:
•‫ﺗ‬‫ﺴﺐ‬ ‫ﺤ‬‫ﺔ‬ ‫اﻵﻧﯿ‬ ‫ﺪرة‬ ‫اﻟﻘ‬‫ﺔ‬ ‫اﻟﻔﻮﻟﻄﯿ‬ ‫ﺮب‬ ‫ﺿ‬ ‫ﻞ‬ ‫ﺣﺎﺻ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﺼﺮف‬ ‫اﻟ‬ ‫ﺔ‬ ‫اﻟﻤﻘﺎوﻣ‬ ‫ﻲ‬ ‫ﻓ‬‫ﺔ‬ ‫اﻵﻧﯿ‬)VR(‫ﺎر‬ ‫اﻟﺘﯿ‬ ‫ﻲ‬ ‫ﻓ‬‫ﻲ‬ ‫اﻵﻧ‬)IR(
‫ﺑﯿ‬ ‫واﻟﻌﻼﻗﺔ‬‫اوم‬ ‫ﻗﺎﻧﻮن‬ ‫ﺣﺴﺐ‬ ‫ﻨﮭﻢ‬)VR=IR . R(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬:
•‫ﺗ‬‫ﺤﺴﺐ‬‫اﻟﻌﻈﻤﻰ‬ ‫اﻟﻘﺪرة‬‫اﻟﻌﻈﻤﻰ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﺿﺮب‬ ‫ﺣﺎﺻﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺼﺮف‬ ‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﻓﻲ‬)Vm(‫اﻟﺘﯿﺎر‬ ‫ﻓﻲ‬‫اﻷﻋﻈﻢ‬)Im(
‫اوم‬ ‫ﻗﺎﻧﻮن‬ ‫ﺣﺴﺐ‬ ‫ﺑﯿﻨﮭﻢ‬ ‫واﻟﻌﻼﻗﺔ‬)Vm=Im . R(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬:
•‫ا‬ ‫اﻣﺎ‬‫اﻟﻌﻼﻗﺎت‬ ‫ﻣﻦ‬ ‫وﺗﺤﺴﺐ‬ ‫اﻟﻌﻈﻤﻰ‬ ‫اﻟﻘﺪرة‬ ‫ﻧﺼﻒ‬ ‫ﻓﺘﺴﺎوي‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫ﻟﻘﺪرة‬:
‫ان‬ ‫أي‬:
‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬:
‫س‬/‫؟‬ ‫اﻟﻌﻈﻤﻰ‬ ‫اﻟﻘﺪرة‬ ‫ﻧﺼﻒ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﻘﺪرة‬ ‫ان‬ ‫اﺛﺒﺖ‬
‫ج‬/
mavmmav
2
2
mmmmRRR
P
2
1
PV.I
2
1
P
2
1
)t(sin
)t(sinV.I)tsin(V.)tsin(IV.IP
=⇒=∴
=ω
ω=ωω==
Q
v‫اﻟﻘﺪرة‬ ‫ﻋﺎﻣﻞ‬)Pf(‫ﻻن‬ ‫واﺣﺪ‬ ‫ﯾﺴﺎوي‬)0=φ(‫وان‬)10coscosPf ==φ=(
mav P
2
1
P =
R
V
PorR.IPorVIP
R
V
2
1
PorR.I
2
1
PorV.I
2
1
P
2
eff
av
2
effaveffeffav
2
m
av
2
mavmmav
===
===
R
V
PorR.IPorV.IP
2
m
m
2
mmmmm ===
R
V
PorR.IPorV.IP
2
R
R
2
RRRRR ===

34. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-35-
‫ﺻﺮف‬ ‫ﻣﺤﺚ‬ ‫ﻓﻴﻬﺎ‬ ‫اﻟﺤﻤﻞ‬ ‫ﻣﺘﻨﺎوب‬ ‫ﺗﻴﺎر‬ ‫داﺋﺮة‬:
v‫اﻟـــﺼﺮف‬ ‫اﻟﻤﺤـــﺚ‬ ‫ﻓـــﻲ‬ ‫ﻟﻠﻔﻮﻟﻄﻴـــﺔ‬ ‫اﻟﻄـــﻮر‬ ‫ﻣﺘﺠـــﻪ‬)VL(‫ﻟﻠﺘﻴـــﺎر‬ ‫اﻟﻄـــﻮر‬ ‫ﻣﺘﺠـــﻪ‬ ‫ﻳـــﺴﺒﻖ‬)IL(‫ﻃـــﻮر‬ ‫ﻓـــﺮق‬ ‫ﺑﺰاوﻳـــﺔ‬
)
2
or90
π
=φ°=φ(‫ﻟﻠﺘﻴـﺎر‬ ‫اﻟﻄـﻮر‬ ‫ﻣﺘﺠـﻪ‬ ‫او‬ ‫اﺳـﺎس‬ ‫ﻛﻤﺘﺠـﻪ‬ ‫اﻟﺘﻴـﺎر‬ ‫ﻳﺆﺧـﺬ‬ ‫ﻋﻨﺪﻣﺎ‬)IL(‫ﻋـﻦ‬ ‫ﻳﺘـﺎﺧﺮ‬‫اﻟﻄـﻮر‬ ‫ﻣﺘﺠـﻪ‬
‫ﻟﻠﻔﻮﻟﻄﻴﺔ‬)VL(‫ﻃﻮر‬ ‫ﻓﺮق‬ ‫ﺑﺰاوﻳﺔ‬)
2
or90
π
=φ°=φ(‫اﺳﺎس‬ ‫ﻛﻤﺘﺠﻪ‬ ‫اﻟﻔﻮﻟﻄﻴﺔ‬ ‫ﺗﺆﺧﺬ‬ ‫ﻋﻨﺪﻣﺎ‬.
‫ﺗﻨﻮﻳﻪ‬/‫اﻟﻤﺤﻮر‬ ‫ﻣﻦ‬ ‫اﻟﻤﻮﺟﺐ‬ ‫اﻻﺗﺠﺎه‬ ‫ﻋﻠﻰ‬ ‫ﻳﻨﻄﺒﻖ‬ ‫اﻟﺬي‬ ‫اﻟﻤﺘﺠﻪ‬ ‫ﻫﻮ‬ ‫اﻻﺳﺎس‬ ‫اﻟﻤﺘﺠﻪ‬)X. (
v‫اﻟﻄﻮرﻳﺔ‬ ‫اﻟﻤﻌﺎدﻻت‬)‫اﻻﻧﻴﺔ‬(‫ﺑﺎﻟﻌﻼﻗﺎت‬ ‫ﻋﻨﻬﺎ‬ ‫ﻳﻌﺒﺮ‬ ‫واﻟﺘﻴﺎر‬ ‫ﻟﻠﻔﻮﻟﻄﻴﺔ‬‫اﻻﺗﻴﺔ‬:
v‫اﻟﺤﺚ‬ ‫رادة‬)XL(‫ﻟﻤﺤـﺚ‬:‫ﻫـﻲ‬‫اﻟﻤﻨـﺴﺎب‬ ‫اﻟﺘﻴـﺎر‬ ‫ﺗـﺮدد‬ ‫ﻓـﻲ‬ ‫ﻟﻠﺘﻐﻴـﺮ‬ ‫اﻟﻤﺤـﺚ‬ ‫ﻳﺒـﺪﻳﻬﺎ‬ ‫اﻟﺘـﻲ‬ ‫اﻟﻤﻌﺎﻛـﺴﺔ‬‫ﻓﻴـﻪ‬‫وﺳـﺒﺒﻬﺎ‬
‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬.
‫اﻟﺤﺚ‬ ‫رادة‬ ‫ﺗﺤﺴﺐ‬‫ﻣﺘﻨﺎوب‬ ‫ﺗﻴﺎر‬ ‫ﻓﻴﻪ‬ ‫ﻳﻨﺴﺎب‬ ‫ﻟﻤﻠﻒ‬‫اﻟﻌﻼﻗﺎت‬ ‫ﻣﻦ‬‫اﻟﺮﻳﺎﺿﻴﺔ‬‫اﻟﺘﺎﻟﻴﺔ‬:
or
‫ﺣﯿﺚ‬:
ω:‫ووﺣﺪﺗﮫ‬ ‫اﻟﺰاوي‬ ‫اﻟﺘﺮدد‬rad/s‫ﺣﯿﺚ‬)f2π=ω. (
L:‫ھﻨﺮي‬ ‫ووﺣﺪﺗﮫ‬ ‫ﻟﻠﻤﺤﺚ‬ ‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬)H. (
f:‫اﻟﻤﺼﺪر‬ ‫ﺗﺮدد‬ ‫او‬ ‫اﻟﺘﯿﺎر‬ ‫ﺗﺮدد‬ ‫او‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﺗﺮدد‬‫ھﺮﺗﺰ‬ ‫ووﺣﺪﺗﮫ‬)Hz(
♦‫ان‬ ‫ﺑﻤﺎ‬:
v‫اﻟﻘﺪرة‬ ‫ﻋﺎﻣﻞ‬)Pf(‫ﻳﺴﺎوي‬)φcos(‫وﻳﺴﺎوي‬)cos90º(‫ﺻﻔﺮ‬ ‫وﻳﺴﺎوي‬.
)90tsin(IIor)tsin(II
)tsin(VV)90tsin(VV
mLmL
mLmL
°−ω=ω=
ω=°+ω=
1
2
1L
2L
L
L
L
X
X
)ttancons(LX =⇒=ωα
1
2
1L
2L
L
X
X
)ttanconsL(X
ω
ω
=⇒=ωα
Lf2XorLX LL π=ω=
L
L
L
I
V
X = ‫اوم‬ ‫ﻗﺎﻧﻮن‬ ‫ﺣﺴﺐ‬
‫اﻟﻌﻮاﻣﻞ‬ ‫ﺣﺴﺐ‬

35. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-36-
‫ﺻﺮف‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﻓﻴﻬﺎ‬ ‫اﻟﺤﻤﻞ‬ ‫ﻣﺘﻨﺎوب‬ ‫ﺗﻴﺎر‬ ‫داﺋﺮة‬:
v‫ﻣﺘﺠﻪ‬‫اﻟﺴﻌﺔ‬ ‫ذات‬ ‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﻓﻲ‬ ‫ﻟﻠﺘﻴﺎر‬ ‫اﻟﻄﻮر‬‫اﻟﺼﺮف‬)IC(‫ﻟﻠﻔﻮﻟﻄﻴـﺔ‬ ‫اﻟﻄـﻮر‬ ‫ﻣﺘﺠﻪ‬ ‫ﻳﺴﺒﻖ‬)VC(‫ﻃـﻮر‬ ‫ﻓـﺮق‬ ‫ﺑﺰاوﻳـﺔ‬
)
2
or90
π
=φ°=φ(‫ﻟﻠﻔﻮﻟﻄﻴﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﻪ‬ ‫او‬ ‫اﺳﺎس‬ ‫ﻛﻤﺘﺠﻪ‬ ‫اﻟﻔﻮﻟﻄﻴﺔ‬ ‫ﺗﺆﺧﺬ‬ ‫ﻋﻨﺪﻣﺎ‬)VC(‫ﻣﺘﺠـﻪ‬ ‫ﻋـﻦ‬ ‫ﻳﺘـﺎﺧﺮ‬
‫ﻟﻠ‬ ‫اﻟﻄﻮر‬‫ﺘﻴﺎر‬)IC(‫ﻃﻮر‬ ‫ﻓﺮق‬ ‫ﺑﺰاوﻳﺔ‬)
2
or90
π
=φ°=φ(‫اﻟﺘﻴﺎر‬ ‫ﻳﺆﺧﺬ‬ ‫ﻋﻨﺪﻣﺎ‬‫اﺳﺎس‬ ‫ﻛﻤﺘﺠﻪ‬.
v‫اﻟﻄﻮرﻳﺔ‬ ‫اﻟﻤﻌﺎدﻻت‬)‫اﻻﻧﻴﺔ‬(‫اﻻﺗﻴﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺎت‬ ‫ﻋﻨﻬﺎ‬ ‫ﻳﻌﺒﺮ‬ ‫واﻟﺘﻴﺎر‬ ‫ﻟﻠﻔﻮﻟﻄﻴﺔ‬:
v‫اﻟﺴﻌﺔ‬ ‫رادة‬)XC(‫ﻟﻤﺘﺴﻌﺔ‬:‫اﻟﺘـﻲ‬ ‫اﻟﻤﻌﺎﻛﺴﺔ‬ ‫ﻫﻲ‬‫ﺗﺒـ‬‫ﻟ‬ ‫اﻟﻤﺘـﺴﻌﺔ‬ ‫ﺪﻳﻬﺎ‬‫ﻓـﻲ‬ ‫ﻠﺘﻐﻴـﺮ‬‫ﺗـﺮدد‬‫اﻟ‬‫ﻔﻮﻟﻄﻴـﺔ‬‫ﻓـﻲ‬ ‫اﻟﻤﻮﺿـﻮﻋﺔ‬
‫اﻟﺪاﺋﺮة‬.
‫اﻟﺴﻌﺔ‬ ‫رادة‬ ‫ﺗﺤﺴﺐ‬‫ﻣﺘﻨﺎوب‬ ‫ﺗﻴﺎر‬ ‫ﻓﻴﻬﺎ‬ ‫ﻳﻤﺮ‬ ‫ﻟﻤﺘﺴﻌﺔ‬‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻣﻦ‬:
or
‫ﺣﯿﺚ‬:
ω:‫ووﺣﺪﺗﮫ‬ ‫اﻟﺰاوي‬ ‫اﻟﺘﺮدد‬rad/s‫ﺣﯿﺚ‬)f2π=ω. (
C:‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺳﻌﺔ‬‫ووﺣﺪﺗﮭ‬‫ﺎ‬‫ﻓﺎراد‬)F(.
f:‫ھﺮﺗﺰ‬ ‫ووﺣﺪﺗﮫ‬ ‫اﻟﻤﺼﺪر‬ ‫ﺗﺮدد‬ ‫او‬ ‫اﻟﺘﯿﺎر‬ ‫ﺗﺮدد‬ ‫او‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﺗﺮدد‬)Hz(
♦‫ان‬ ‫ﺑﻤﺎ‬:
v‫اﻟﻘﺪرة‬ ‫ﻋﺎﻣﻞ‬)Pf(‫ﻳﺴﺎو‬‫ي‬)φcos(‫وﻳﺴﺎوي‬)cos90º(‫ﺻﻔﺮ‬ ‫وﻳﺴﺎوي‬.
)90tsin(VVor)tsin(IV
)tsin(II)90tsin(II
mCmC
mCmC
°−ω=ω=
ω=°+ω=
2
1
1C
2C
C
C
C
X
X
)ttancons(
C
1
X =⇒=ωα
2
1
1C
2C
C
X
X
)ttanconsC(
1
X
ω
ω
=⇒=
ω
α
Cf2
1
Xor
C
1
X CC
π
=
ω
=
C
C
C
I
V
X = ‫اوم‬ ‫ﻗﺎﻧﻮن‬ ‫ﺣﺴﺐ‬
‫اﻟﻌﻮاﻣﻞ‬ ‫ﺣﺴﺐ‬

36. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-37-
‫س‬/‫ﺻﺮف؟‬ ‫ﺳﻌﺔ‬ ‫ذات‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﺗﺤﺘﻮي‬ ‫ﻣﺘﻨﺎوب‬ ‫ﺗﯿﺎر‬ ‫ﻟﺪاﺋﺮة‬ ‫اﻟﺘﯿﺎر‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫اﺷﺘﻖ‬
‫ج‬/
)
2
tsin(II)tcos(II
)tcos(
X
V
)tcos(V.
X
1
)tcos(VC
t
)tsin(
VC
t
)tsin(V
.C
t
V
.C
t
)V.C(
t
Q
I
mCmC
C
m
m
C
m
m
mCC
C
π
+ω=⇒ω=∴
ω=ω=ωω=
∆
ω∆
=
∆
ω∆
=
∆
∆
=
∆
∆
=
∆
∆
=
‫ﺗﺤﺘﻮي‬ ‫ﻣﺘﻨﺎوب‬ ‫ﺗﻴﺎر‬ ‫داﺋﺮة‬‫ﻣﺘﻮ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﺛﻼﺛﺔ‬ ‫او‬ ‫ﻋﻨﺼﺮﻳﻦ‬‫اﻟﻴﺔ‬‫ﻣﺘﻮا‬ ‫او‬‫زﻳﺔ‬‫اﻟﺮﺑﻂ‬:
‫ﺼﺮﯾﻦ‬ ‫ﻋﻨ‬ ‫ﻂ‬ ‫رﺑ‬ ‫ﺔ‬ ‫ﺣﺎﻟ‬ ‫ﻲ‬ ‫ﻓ‬)R-L(‫او‬)R-C(‫ﺮ‬ ‫ﻋﻨﺎﺻ‬ ‫ﺔ‬ ‫ﺛﻼﺛ‬ ‫او‬)R-L-C(‫ﻮازي‬ ‫اﻟﺘ‬ ‫ﻰ‬ ‫ﻋﻠ‬ ‫او‬ ‫ﻮاﻟﻲ‬ ‫اﻟﺘ‬ ‫ﻰ‬ ‫ﻋﻠ‬‫ﺼﺪر‬ ‫ﻣ‬ ‫ﻰ‬ ‫اﻟ‬
‫ﻣﺘﻨ‬‫ا‬ ‫ﻣﻦ‬ ‫ﻧﺘﺨﺬ‬ ‫ﻓﺎﻧﻨﺎ‬ ‫ﺎوب‬‫ﻟﻤﺤﻮر‬x‫اﺳﻨﺎد‬ ‫ﻣﺤﻮر‬)‫ﻣﺮﺟﻌﻲ‬ ‫ﻣﺤﻮر‬(‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﯾﻨﻄﺒﻖ‬ ‫وﻋﻨﺪﻣﺎ‬)‫ﻮاﻟﻲ‬‫اﻟﺘ‬ ‫ﻂ‬‫رﺑ‬ ‫ﻲ‬‫ﻓ‬(‫او‬
‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬)‫اﻟﺘﻮازي‬ ‫رﺑﻂ‬ ‫ﻓﻲ‬(‫اﺳﺎس‬ ‫ﻣﺘﺠﮫ‬ ‫ﯾﺴﻤﻰ‬ ‫اﻟﻤﺮﺟﻊ‬ ‫اﻟﻤﺤﻮر‬ ‫ﻋﻠﻰ‬.
‫اوﻻ‬:‫اﻟﻌﻨﺎﺻ‬ ‫رﺑﻂ‬‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫ﺮ‬:
•‫ﻟﻠﺘﯿﺎرات‬ ‫اﻟﻄﻮرﯾﺔ‬ ‫اﻟﻤﺘﺠﮭﺎت‬)IR , IL , IC(‫ﻋﻠﻰ‬ ‫ﺗﻨﻄﺒﻖ‬‫اﻻﺳﻨﺎد‬ ‫ﻣﺤﻮر‬ ‫ﻣﻦ‬ ‫اﻟﻤﻮﺟﺐ‬ ‫اﻻﺗﺠﺎه‬)‫اﻟﻤﺤﻮر‬x(.
•‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮرﯾﺔ‬ ‫اﻟﻤﺘﺠﮭﺎت‬)VR , VL , VC(‫طﻮر‬ ‫ﻓﺮق‬ ‫زاوﯾﺔ‬ ‫ﻣﻨﮭﺎ‬ ‫ﻛﻞ‬ ‫ﯾﺼﻨﻊ‬φ‫اﻟﻤﺤﻮر‬ ‫ﻣﻊ‬x.
‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﻨﺎﺻﺮ‬ ‫رﺑﻂ‬ ‫ﺧﻮاص‬:
1-‫ﻣﻘﺪا‬‫ﺟﻤ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺴﺎوي‬‫ﻣﺘ‬ ‫اﻟﺘﯿﺎر‬ ‫ر‬‫ﺪاﺋﺮة‬‫اﻟ‬ ‫ﺮ‬‫ﻋﻨﺎﺻ‬ ‫ﻊ‬‫ﯿ‬‫ﻲ‬‫اﻟﻜﻠ‬ ‫ﺎر‬‫اﻟﺘﯿ‬ ‫ﺴﺎوي‬‫وﯾ‬)‫ﺴﻲ‬‫اﻟﺮﺋﯿ‬ ‫ﺎر‬‫اﻟﺘﯿ‬(‫ﮫ‬‫ﻣﺘﺠ‬ ‫ﻢ‬‫ﻧﺮﺳ‬ ‫ﺬﻟﻚ‬‫ﻟ‬‫ﻮر‬‫اﻟﻄ‬
‫ﻟﻠﺘﯿﺎر‬‫ﻣﺤﻮر‬ ‫ﻋﻠﻰ‬‫اﻹﺳﻨﺎد‬)‫ﻛﺄﺳﺎس‬. (
‫ان‬ ‫اي‬:
‫ﺖ‬‫ﺑ‬‫ﺎ‬‫ﺛ‬IIIII TCLR ====
2-‫ﺪ‬ ‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺪار‬‫ﻣﻘ‬‫ﻰ‬‫إﻟ‬ ‫ﺼﺮ‬ ‫ﻋﻨ‬ ‫ﻦ‬‫ﻣ‬ ‫ﻒ‬‫ﯾﺨﺘﻠ‬‫ﺮ‬‫آﺧ‬‫ﺬﻟﻚ‬‫ﻟ‬‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺔ‬ ‫اﻟﻔﻮﻟﻄﯿ‬ ‫ﺴﺎب‬‫ﻟﺤ‬)‫ﺼﻠﺔ‬ ‫اﻟﻤﺤ‬ ‫ﺔ‬‫اﻟﻔﻮﻟﻄﯿ‬(‫ﻲ‬‫واﻟﺘ‬‫ﺎ‬ ‫رﻣﺰھ‬
)TV(‫طﻮرﯾﺎ‬ ‫ﺟﻤﻌﺎ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻟﻌﻨﺎﺻﺮ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮوق‬ ‫ﻧﺠﻤﻊ‬)‫اﺗﺠﺎھﯿﺎ‬(‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫زاوﯾﺔ‬ ‫وﺟﻮد‬ ‫ﺑﺴﺒﺐ‬‫ﺔ‬‫ﻣﺒﺮھﻨ‬ ‫ﻖ‬‫ﺑﺘﻄﺒﯿ‬ ‫ﻚ‬‫وذﻟ‬
‫ادﻧﺎه‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﻣﺨﻄﻂ‬ ‫ﻣﻦ‬ ‫ﻓﯿﺜﺎﻏﻮرس‬:
‫وﺣﺴﺐ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﻣﺨﻄﻄﺎت‬
‫اﻟﺮﺑﻂ‬ ‫اﻟﻤﺘﻮاﻟﯿﺔ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻋﻨﺎﺻﺮ‬

37. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-38-
‫ﻣﺒﺮھ‬ ‫ﻖ‬‫وﺑﺘﻄﺒﯿ‬ ‫اﻋﻼه‬ ‫اﻟﻤﺨﻄﻄﺎت‬ ‫ﻣﻦ‬‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺔ‬‫اﻟﻔﻮﻟﻄﯿ‬ ‫ﺪ‬‫ﻧﺠ‬ ‫ﺎﻏﻮرس‬‫ﻓﯿﺜ‬ ‫ﺔ‬‫ﻨ‬‫ﺼﻠﺔ‬‫اﻟﻤﺤ‬ ‫ﺔ‬‫اﻟﻔﻮﻟﻄﯿ‬ ‫او‬)TV(‫ﺮ‬‫ﻋﻨﺎﺻ‬ ‫ﺴﺐ‬‫وﺣ‬
‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اﻟﺪاﺋﺮة‬:
‫ﺣﯿﺚ‬:
XV:‫وﺗ‬ ‫ﺼﻠﺔ‬ ‫اﻟﻤﺤ‬ ‫ﺮادة‬ ‫اﻟ‬ ‫ﺔ‬ ‫ﻓﻮﻟﻄﯿ‬‫ﺮادﺗﯿﻦ‬ ‫اﻟ‬ ‫ﺔ‬ ‫ﻓﻮﻟﻄﯿ‬ ‫ﯿﻦ‬ ‫ﺑ‬ ‫ﺮق‬ ‫اﻟﻔ‬ ‫ﺴﺎوي‬)‫ﺴﻌﺔ‬ ‫اﻟ‬ ‫ورادة‬ ‫ﺚ‬ ‫اﻟﺤ‬ ‫رادة‬(
‫ان‬ ‫أي‬:)CLX VVV −=(
‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫زاوﯾﺔ‬ ‫ﺣﺴﺎب‬ ‫ﯾﻤﻜﻦ‬ ‫ﻛﺬﻟﻚ‬)φ(‫اﻟﻔﻮﻟﻄﯿ‬ ‫ﺑﯿﻦ‬‫اﻟﻜﻠﯿﺔ‬ ‫ﺔ‬)‫اﻟﻤﺤﺼﻠﺔ‬(‫ﻣﻦ‬ ‫واﻟﺘﯿﺎر‬)φtan(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬:
‫اﻟﻘﺪرة‬ ‫ﻋﺎﻣﻞ‬ ‫ﻟﺤﺴﺎب‬ ‫اﻣﺎ‬)pf(‫ﻓﻨﺴﺘﺨﺪم‬)φcos(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬:
‫ﻟﺤﻈﺔ‬ ‫اﯾﺔ‬ ‫ﻓﻲ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﻻﯾﺠﺎد‬ ‫اﻣﺎ‬)‫اﻻﻧﯿﺔ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬(‫ﺔ‬‫ﻟﺤﻈ‬ ‫ﺔ‬‫اﯾ‬ ‫ﻲ‬‫ﻓ‬ ‫واﻟﺘﯿﺎر‬)‫ﻲ‬‫اﻻﻧ‬ ‫ﺎر‬‫اﻟﺘﯿ‬(‫ﺴﺘﺨﺪم‬‫ﻓﻨ‬‫ﺎدﻻت‬‫ﻣﻌ‬
‫اﻻﺗﯿﺔ‬ ‫واﻟﺘﯿﺎر‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬:
‫ﺣﯿﺚ‬:
f2,V2V,I2I effmeffm π=ω==
‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﺗﻤﺜﻞ‬ ‫اﻟﻤﺆﺛﺮة‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬)‫اﻟﻤﺤﺼﻠﺔ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬) (TV(‫اﻟﺮﺋﯿﺴﻲ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﺗﯿﺎر‬ ‫ﯾﻤﺜﻞ‬ ‫اﻟﻤﺆﺛﺮ‬ ‫واﻟﺘﯿﺎر‬)I.(
‫اﻟﺮﺑﻊ‬‫اﻟﺮاﺑﻊ‬)tsin(VV
or
‫اﻟﺮﺑﻊ‬‫اﻻول‬)tsin(VV
‫اﺳﺎس‬)tsin(II
m)ins(T
m)ins(T
mins
φ−ω=
φ+ω=
ω=
2
C
2
R
2
T
2
L
2
R
2
T
2
X
2
R
2
T
2
CL
2
R
2
T
VVV
or
VVV
or
VVVor)VV(VV
+=
+=
+=−+=
T
R
V
V
cospf =φ=
)CR()LR()CLR(
V
V
tanor
V
V
tanor
V
VV
tan
R
C
R
L
R
CL
−−−−
−
=φ=φ
−
=φ
‫ﻟﺪاﺋﺮة‬)R-L-C(‫اﻟﺤﺜﯿﺔ‬ ‫ﻟﻠﺨﻮاص‬
‫اﻟﺴﻌﻮﯾﺔ‬ ‫او‬.
‫ﻟﺪاﺋﺮة‬)R-L(
‫ﻟﺪاﺋﺮة‬)R-C(
‫داﺋﺮة‬)R-L-C(‫داﺋﺮة‬ ‫او‬ ‫اﻟﺤﺜﯿﺔ‬ ‫ﻟﻠﺨﻮاص‬)R-L. (
‫داﺋﺮة‬)R-L-C(‫داﺋﺮة‬ ‫او‬ ‫اﻟﺴﻌﻮﯾﺔ‬ ‫ﻟﻠﺨﻮاص‬)R-C(
.

38. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
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‫ﻣﻼﺣﻈﺎت‬/
a-‫ﻛﺎﻧﺖ‬ ‫اذا‬VL > VC‫ﻓﺎن‬:
•‫ﺣﺜﯿﺔ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﺧﻮاص‬‫اﻟﻤﺤﺼﻠﺔ‬ ‫اﻟﺮادة‬ ‫ﻓﻮﻟﻄﯿﺔ‬ ‫وان‬)VX(‫ﻣﻮﺟﺒﺔ‬
•‫ﻓﺮق‬ ‫زاوﯾﺔ‬‫اﻟﻄﻮر‬)φ(‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﺑﯿﻦ‬)VT(‫ﮫ‬‫وﻣﺘﺠ‬
‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬)I(‫ﻣﻮﺟﺒﺔ‬
•‫ﺮق‬‫ﻓ‬ ‫ﺔ‬ ‫ﺑﺰاوﯾ‬ ‫ﺎر‬ ‫ﻟﻠﺘﯿ‬ ‫ﻮر‬ ‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫ﺴﺒﻖ‬ ‫ﯾ‬ ‫ﺔ‬ ‫اﻟﻜﻠﯿ‬ ‫ﺔ‬ ‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫ﻮر‬ ‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬
‫طﻮر‬)φ.(
•‫اﻷول‬ ‫اﻟﺮﺑﻊ‬ ‫ﻓﻲ‬ ‫ﯾﺮﺳﻢ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﻣﺜﻠﺚ‬)‫اﻷﻋﻠﻰ‬ ‫ﻧﺤﻮ‬(
b-‫ﻛﺎﻧﺖ‬ ‫اذا‬VL < VC‫ﻓﺎن‬:
•‫ﺳﻌﻮﯾﺔ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﺧﻮاص‬‫اﻟﻤﺤﺼﻠﺔ‬ ‫اﻟﺮادة‬ ‫ﻓﻮﻟﻄﯿﺔ‬ ‫وان‬)VX(‫ﺳﺎﻟﺒﺔ‬
•‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫زاوﯾﺔ‬)φ(‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﺑﯿﻦ‬)VT(‫ﮫ‬‫وﻣﺘﺠ‬
‫ﺳﺎﻟﺒﺔ‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬
•‫ﺄﺧﺮ‬‫ﯾﺘ‬ ‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺔ‬‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬)‫ﻒ‬‫ﯾﺘﺨﻠ‬(‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫ﻦ‬‫ﻋ‬
‫طﻮر‬ ‫ﻓﺮق‬ ‫ﺑﺰاوﯾﺔ‬)φ.(
•‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﻣﺜﻠﺚ‬‫اﻟﺮاﺑﻊ‬ ‫اﻟﺮﺑﻊ‬ ‫ﻓﻲ‬ ‫ﯾﺮﺳﻢ‬)‫اﻷﺳﻔﻞ‬ ‫ﻧﺤﻮ‬(
c-‫ﻛﺎﻧﺖ‬ ‫اذا‬VL = VC‫ﻓﺎن‬:
•‫ﺮف‬ ‫ﺻ‬ ‫ﺔ‬ ‫اوﻣﯿ‬ ‫ﺔ‬ ‫ﻣﻘﺎوﻣ‬ ‫ﻮاص‬ ‫ﺧ‬ ‫ﺪاﺋﺮة‬ ‫اﻟ‬ ‫ﻮاص‬ ‫ﺧ‬‫ﺮادة‬ ‫اﻟ‬ ‫ﺔ‬ ‫ﻓﻮﻟﻄﯿ‬ ‫وان‬
‫اﻟﻤﺤﺼﻠﺔ‬)VX(‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬
•‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫زاوﯾﺔ‬)φ(‫اﻟﻜﻠﯿﺔ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﺑﯿﻦ‬)VT(‫وﻣﺘﺠﮫ‬
‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬
•‫ﺔ‬ ‫اﻟﻜﻠﯿ‬ ‫ﺔ‬ ‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫ﻮر‬ ‫اﻟﻄ‬ ‫ﮫ‬ ‫ﻣﺘﺠ‬‫ﺎر‬ ‫ﻟﻠﺘﯿ‬ ‫ﻮر‬ ‫اﻟﻄ‬ ‫ﮫ‬ ‫ﻣﺘﺠ‬ ‫ﻰ‬ ‫ﻋﻠ‬ ‫ﻖ‬ ‫ﯾﻨﻄﺒ‬
)‫واﺣﺪ‬ ‫طﻮر‬ ‫ﻓﻲ‬ ‫اﻧﮭﻤﺎ‬ ‫أي‬(

39. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-40-
3-‫ورﻣﺰھﺎ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻓﻲ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻤﻤﺎﻧﻌﺔ‬)Z(‫ﻓﺘﺤﺴﺐ‬‫وذﻟﻚ‬ ‫اﻟﻤﻤﺎﻧﻌﺔ‬ ‫ﻣﺨﻄﻂ‬ ‫ﻣﻦ‬‫ﺑ‬‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫ﻓﯿﺜﺎﻏﻮرس‬ ‫ﻣﺒﺮھﻨﺔ‬ ‫ﺘﻄﺒﯿﻖ‬:
‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻤﻤﺎﻧﻌﺔ‬ ‫ﻧﺠﺪ‬ ‫ﻓﯿﺜﺎﻏﻮرس‬ ‫ﻣﺒﺮھﻨﺔ‬ ‫وﺑﺘﻄﺒﯿﻖ‬ ‫اﻋﻼه‬ ‫اﻟﻤﺨﻄﻄﺎت‬ ‫ﻣﻦ‬)Z(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻋﻨﺎﺻﺮ‬ ‫وﺣﺴﺐ‬:
‫ﺣﯿﺚ‬:
X:‫ﺼﻠﺔ‬ ‫اﻟﻤﺤ‬ ‫ﺮادة‬ ‫اﻟ‬‫ﺎﻻوم‬ ‫ﺑ‬ ‫ﺎس‬ ‫وﺗﻘ‬)Ω(‫ﺮادﺗﯿﻦ‬ ‫اﻟ‬ ‫ﯿﻦ‬ ‫ﺑ‬ ‫ﺮق‬ ‫اﻟﻔ‬ ‫ﺴﺎوي‬ ‫وﺗ‬)‫ورادة‬ ‫ﺚ‬ ‫اﻟﺤ‬ ‫رادة‬‫ﺴﻌﺔ‬ ‫اﻟ‬(
‫ان‬ ‫أي‬:)CL XXX −=(
Z:‫ﺎﻻوم‬‫ﺑ‬ ‫ﺎس‬‫وﺗﻘ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻣﺮور‬ ‫ﺿﺪ‬ ‫واﻟﻤﻘﺎوﻣﺔ‬ ‫ﻟﻠﺮادة‬ ‫اﻟﻤﺸﺘﺮﻛﺔ‬ ‫اﻟﻤﻌﺎﻛﺴﺔ‬ ‫ﺑﺎﻧﮭﺎ‬ ‫وﺗﻌﺮف‬ ‫ﻟﻠﺪاﺋﺮة‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻤﻤﺎﻧﻌﺔ‬
‫ﻣﻘﺎوﻣﺔ‬ ‫ﻟﯿﺴﺖ‬ ‫ﻟﻜﻨﮭﺎ‬ ‫اوم‬ ‫ﻗﺎﻧﻮن‬ ‫اﻟﻰ‬ ‫وﺗﺨﻀﻊ‬.
‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫زاوﯾﺔ‬ ‫ﺣﺴﺎب‬ ‫ﯾﻤﻜﻦ‬ ‫ﻛﺬﻟﻚ‬)φ(‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﺑﯿﻦ‬)‫اﻟﻤﺤﺼﻠﺔ‬(‫ﻣﻦ‬ ‫واﻟﺘﯿﺎر‬)φtan(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬:
)CR()LR()CLR(
R
X
tanor
R
X
tanor
R
XX
tan CLCL
−−−−
−
=φ=φ
−
=φ
2
C
22
2
L
22
2222
CL
22
XRZ
or
XRZ
or
XRZor)XX(RZ
+=
+=
+=−+=
‫اﻟﻤﻤ‬ ‫ﻣﺨﻄﻄﺎت‬‫وﺣﺴﺐ‬ ‫ﺎﻧﻌﺔ‬
‫اﻟﺮﺑﻂ‬ ‫اﻟﻤﺘﻮاﻟﯿﺔ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻋﻨﺎﺻﺮ‬
‫ﻟﺪاﺋﺮة‬)R-L-C(‫اﻟﺤﺜﯿﺔ‬ ‫ﻟﻠﺨﻮاص‬
‫اﻟﺴﻌﻮﯾﺔ‬ ‫او‬.
‫ﻟﺪاﺋﺮة‬)R-L(
‫ﻟﺪاﺋﺮة‬)R-C(

40. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-41-
‫اﻟﻘﺪرة‬ ‫ﻋﺎﻣﻞ‬ ‫ﻟﺤﺴﺎب‬ ‫اﻣﺎ‬)pf(‫ﻓﻨﺴﺘﺨﺪم‬)φcos(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬:
‫ﻗﺎﻧﻮ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫ﻛﺬﻟﻚ‬‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اﻟﺴﻌﺔ‬ ‫ورادة‬ ‫اﻟﺤﺚ‬ ‫ورادة‬ ‫واﻟﻤﻘﺎوﻣﺔ‬ ‫ﻟﻠﺪاﺋﺮة‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻤﻤﺎﻧﻌﺔ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﻧﺠﺪ‬ ‫ان‬ ‫ﯾﻤﻜﻦ‬ ‫اوم‬ ‫ن‬:
‫ﻣﻼﺣﻈﺎت‬/
1-‫ﻛﺎﻧﺖ‬ ‫اذا‬XL > XC‫ﻓﺎن‬:
•‫ﺣﺜﯿﺔ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﺧﻮاص‬‫اﻟﻤﺤﺼﻠﺔ‬ ‫اﻟﺮادة‬ ‫وان‬)X(‫ﻣﻮﺟﺒﺔ‬
•‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫زاوﯾﺔ‬)φ(‫ﻣﺘﺠﮫ‬ ‫ﺑﯿﻦ‬‫اﻟﻜﻠﯿﺔ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬)VT(‫وﻣﺘﺠﮫ‬
‫اﻟﻄﻮر‬‫ﻟﻠﺘﯿﺎر‬)I(‫ﻣﻮﺟﺒﺔ‬
•‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬‫ﯾﺴﺒﻖ‬ ‫اﻟﻜﻠﯿﺔ‬‫ﺑ‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬‫ﺰاوﯾﺔ‬
‫طﻮر‬ ‫ﻓﺮق‬)φ(.
•‫اﻷول‬ ‫اﻟﺮﺑﻊ‬ ‫ﻓﻲ‬ ‫ﯾﺮﺳﻢ‬ ‫اﻟﻤﻤﺎﻧﻌﺔ‬ ‫ﻣﺜﻠﺚ‬)‫اﻷﻋﻠﻰ‬ ‫ﻧﺤﻮ‬(
2-‫ﻛﺎﻧﺖ‬ ‫اذا‬XL < XC‫ﻓﺎن‬:
•‫ﺳﻌﻮﯾﺔ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﺧﻮاص‬‫اﻟﻤﺤﺼﻠﺔ‬ ‫اﻟﺮادة‬ ‫وان‬)X(‫ﺳﺎﻟﺒﺔ‬
•‫ﻮر‬ ‫اﻟﻄ‬ ‫ﺮق‬ ‫ﻓ‬ ‫ﺔ‬ ‫زاوﯾ‬)φ(‫ﺔ‬ ‫اﻟﻜﻠﯿ‬ ‫ﺔ‬ ‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫ﻮر‬ ‫اﻟﻄ‬ ‫ﮫ‬ ‫ﻣﺘﺠ‬ ‫ﯿﻦ‬ ‫ﺑ‬)VT(‫ﮫ‬ ‫وﻣﺘﺠ‬
‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬‫ﺳﺎﻟﺒﺔ‬
•‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬‫اﻟﻜﻠﯿﺔ‬‫ﯾﺘﺄﺧﺮ‬)‫ﯾﺘﺨ‬‫ﻠﻒ‬(‫ﺔ‬‫ﺑﺰاوﯾ‬ ‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫ﻋﻦ‬
‫طﻮر‬ ‫ﻓﺮق‬)φ(.
•‫ﻣﺜﻠ‬‫ﯾﺮﺳ‬ ‫اﻟﻤﻤﺎﻧﻌﺔ‬ ‫ﺚ‬‫اﻟﺮاﺑﻊ‬ ‫اﻟﺮﺑﻊ‬ ‫ﻓﻲ‬ ‫ﻢ‬)‫اﻷﺳﻔﻞ‬ ‫ﻧﺤﻮ‬(
3-‫إذا‬‫ﻛﺎﻧﺖ‬XL = XC‫ﻓﺎن‬:
•‫ﺻﺮف‬ ‫اوﻣﯿﺔ‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺧﻮاص‬ ‫اﻟﺪاﺋﺮة‬ ‫ﺧﻮاص‬‫اﻟﻤﺤﺼﻠﺔ‬ ‫واﻟﺮادة‬)X=0(.
•‫ﻮر‬ ‫اﻟﻄ‬ ‫ﺮق‬ ‫ﻓ‬ ‫ﺔ‬ ‫زاوﯾ‬)φ(‫ﺔ‬ ‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫ﻮر‬ ‫اﻟﻄ‬ ‫ﮫ‬ ‫ﻣﺘﺠ‬ ‫ﯿﻦ‬ ‫ﺑ‬)VT(‫ﻮر‬ ‫اﻟﻄ‬ ‫ﮫ‬ ‫وﻣﺘﺠ‬
‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ ‫ﻟﻠﺘﯿﺎر‬.
•‫اﻟﻜﻠﯿ‬ ‫ﺔ‬ ‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫ﻮر‬ ‫اﻟﻄ‬ ‫ﮫ‬ ‫ﻣﺘﺠ‬‫ﺎر‬ ‫ﻟﻠﺘﯿ‬ ‫ﻮر‬ ‫اﻟﻄ‬ ‫ﮫ‬ ‫ﻣﺘﺠ‬ ‫ﻰ‬ ‫ﻋﻠ‬ ‫ﻖ‬ ‫ﯾﻨﻄﺒ‬ ‫ﺔ‬
)‫واﺣﺪ‬ ‫طﻮر‬ ‫ﻓﻲ‬ ‫اﻧﮭﻤﺎ‬ ‫أي‬. (
I
V
X,
I
V
X,
I
V
R,
I
V
Z C
C
L
L
RT
====
Z
R
cospf =φ=

41. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-42-
app
real
P
P
Pf =
‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﻘﺪرة‬:‫ﺑﺎﻟﻮاط‬ ‫وﺗﻘﺎس‬ ‫اﻟﻤﻘﺎوﻣﺔ‬ ‫طﺮﻓﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺴﺘﮭﻠﻜﺔ‬ ‫اﻟﻘﺪرة‬ ‫ھﻲ‬.
‫اﻟﻌﻼﻗﺎت‬ ‫ﻣﻦ‬ ‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﻘﺪرة‬ ‫ﺗﺤﺴﺐ‬‫اﻟﺘﺎﻟﯿﺔ‬:
‫ﺿﺮب‬ ‫ﺣﺎﺻﻞ‬ ‫وﯾﺴﻤﻰ‬‫اﻟﻜﻠ‬ ‫اﻟﺘﯿﺎر‬‫ﻲ‬‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ﻓﻲ‬)TT VI(‫ﺑﺎﻟﺮﻣﺰ‬ ‫ﻟﮭﺎ‬ ‫وﯾﺮﻣﺰ‬ ‫اﻟﻈﺎھﺮﯾﺔ‬ ‫ﺑﺎﻟﻘﺪرة‬)Papp. (
‫اﻟﻈﺎھﺮﯾﺔ‬ ‫اﻟﻘﺪرة‬:‫ﻟﻠﺪاﺋﺮة‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﯿﺎر‬ ‫ﻣﺼﺪر‬ ‫ﯾﺠﮭﺰھﺎ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻘﺪرة‬ ‫ھﻲ‬‫ﺑﺄﻛﻤﻠﮭﺎ‬‫ﺑﺎﻟﻔﻮﻟﻂ‬ ‫وﺗﻘﺎس‬‫أﻣﺒﯿﺮ‬)VA(
‫اﻟﺘﺎﻟﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻣﻦ‬ ‫وﺗﺤﺴﺐ‬:
‫ﻋ‬‫ﺪرة‬ ‫اﻟﻘ‬ ‫ﻞ‬ ‫ﺎﻣ‬)Power factor(:‫ﺴﺒﺔ‬ ‫ﻧ‬ ‫ﻮ‬ ‫ھ‬‫اﻟ‬‫ﻘ‬‫ﺔ‬ ‫اﻟﺤﻘﯿﻘﯿ‬ ‫ﺪرة‬)Preal(‫ﻰ‬ ‫اﻟ‬‫ﺔ‬ ‫اﻟﻈﺎھﺮﯾ‬ ‫ﺪرة‬ ‫اﻟﻘ‬)Papp(‫ﮫ‬ ‫ﻟ‬ ‫ﺰ‬ ‫وﯾﺮﻣ‬)Pf(
‫ان‬ ‫أي‬:
⇒
TT
TT
VI
cosVI
Pf
φ
= ⇒
‫اﻟﻘﺪرة‬ ‫ﻋﺎﻣﻞ‬ ‫ان‬ ‫أي‬)Pf(‫زا‬ ‫ﺗﻤﺎم‬ ‫ﺟﯿﺐ‬ ‫ﯾﺴﺎوي‬‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫وﯾﺔ‬.
‫اﻟﺮﻧﻴ‬ ‫داﺋﺮة‬ ‫ﻣﻤﻴﺰات‬‫ﻦ‬‫اﻟﺮﺑﻂ‬ ‫اﻟﻤﺘﻮاﻟﻴﺔ‬:
1-‫اﻟﺤﺚ‬ ‫رادة‬)XL(‫اﻟﺴﻌﺔ‬ ‫رادة‬ ‫ﺗﺴﺎوي‬)XC(‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻤﺤﺼﻠﺔ‬ ‫ﻓﺎﻟﺮادة‬ ‫ﻟﺬﻟﻚ‬)X=0(‫ﺪاﺋﺮة‬‫اﻟ‬ ‫ﺔ‬‫ﻣﻤﺎﻧﻌ‬ ‫ﻞ‬‫ﯾﺠﻌ‬ ‫وھﺬا‬
‫ﯾﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫اﻗﻞ‬‫اﻟﻤﻘﺎوﻣﺔ‬ ‫وﺗﺴﺎوي‬)Z=R. (
2-‫اﻟﺤﺚ‬ ‫ﻓﻮﻟﻄﯿﺔ‬)VL(‫اﻟﺴﻌﺔ‬ ‫ﻓﻮﻟﻄﯿﺔ‬ ‫ﺗﺴﺎوي‬)VC(‫ﻟﺬﻟﻚ‬‫اﻟﺮ‬ ‫ﻓﻮﻟﻄﯿﺔ‬ ‫ﻓﺎن‬‫اي‬ ‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ ‫اﻟﻤﺤﺼﻠﺔ‬ ‫ادة‬)VT = VR(
3-‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫زاوﯾﺔ‬)φ(‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫ان‬ ‫أي‬ ‫ﻔﺮ‬‫ﺻ‬ ‫ﺴﺎوي‬‫ﺗ‬ ‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫وﻣﺘﺠ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﺑﯿﻦ‬‫ﺔ‬‫اﻟﻔﻮﻟﻄﯿ‬
‫وﻣﺘﻼزﻣﺎن‬ ‫ﻣﺘﻄﺎﺑﻘﺎن‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫وﻣﺘﺠﮫ‬.
4-‫اﻟﻘﺪرة‬ ‫ﻋﺎﻣﻞ‬)Pf(‫ﻻن‬ ‫واﺣﺪ‬ ‫ﯾﺴﺎوي‬:10CosCosPf ==φ=
5-‫ان‬ ‫أي‬ ‫اﻟﻈﺎھﺮﯾﺔ‬ ‫اﻟﻘﺪرة‬ ‫ﺗﺴﺎوي‬ ‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﻘﺪرة‬:Preal = Papp.
6-‫ﻻن‬ ‫ﺻﺮف‬ ‫اوﻣﯿﺔ‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺧﻮاص‬ ‫اﻟﺮﻧﯿﻦ‬ ‫داﺋﺮة‬ ‫ﺗﻤﺘﻠﻚ‬)Z=R.(
7-‫ﻣﻘﺪاره‬ ‫ﻓﻲ‬ ‫ﯾﻜﻮن‬ ‫اﻟﺪاﺋﺮة‬ ‫ﺗﯿﺎر‬‫اﻷﻋﻈﻢ‬‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﻣﻘﺪار‬ ‫ﻋﻠﻰ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻣﻘﺪار‬ ‫وﯾﻌﺘﻤﺪ‬ ‫ﻣﻘﺪار‬ ‫ﺑﺎﻗﻞ‬ ‫اﻟﻤﻤﺎﻧﻌﺔ‬ ‫ﻻن‬
R
V
I T
r =.
8-‫اﻟﺪاﺋﺮة‬ ‫إﻟﻰ‬ ‫اﻟﻤﻨﺘﻘﻠﺔ‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﻘﺪرة‬‫ﺑﺄﻛﺒﺮ‬‫ﻣﻘﺪار‬.
9-‫اﻟﺘﺎﻟﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻣﻦ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻓﻲ‬ ‫اﻟﺮﻧﯿﻨﻲ‬ ‫واﻟﺘﺮدد‬ ‫اﻟﺮﻧﯿﻨﻲ‬ ‫اﻟﺰاوي‬ ‫اﻟﺘﺮدد‬ ‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬:
or
φ
===
cos
P
PorZ.IPorVIP real
app
2
TappTTapp
φ=== cosVIPorR.IPorVIP TTreal
2
RrealRRreal
CL
1
r =ω
CL2
1
fr
π
=
φ= cosPf
‫ﺣﯿﺚ‬:
ωr:‫اﻟﺮﻧﯿﻨﻲ‬ ‫اﻟﺰاوي‬ ‫اﻟﺘﺮدد‬
fr:‫اﻟﺮﻧﯿﻨﻲ‬ ‫اﻟﺘﺮدد‬

42. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-43-
10-‫اﻟﺰاوي‬ ‫اﻟﺘﺮدد‬ ‫ﻧﻄﺎق‬:‫وھ‬‫ﻮ‬‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫ﻟﻠﻘﺪرة‬ ‫اﻷﻋﻈﻢ‬ ‫اﻟﻤﻘﺪار‬ ‫ﻣﻨﺘﺼﻒ‬ ‫ﻋﻨﺪ‬ ‫اﻟﺰاوي‬ ‫اﻟﺘﺮدد‬ ‫ﺑﯿﻦ‬ ‫اﻟﻔﺮق‬.
‫اﻻﺗﯿﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺎت‬ ‫ﻋﻨﮫ‬ ‫ﯾﻌﺒﺮ‬:
(‫اﻟﺘﻌﺮﻳﻒ‬ ‫)ﺑﻤﻮﺟﺐ‬
∆ω:‫اﻟﺰاوي‬ ‫اﻟﺘﺮدد‬ ‫ﻧﻄﺎق‬‫ﺑﻮﺣﺪة‬)rad/sec. (
21
,ωω:‫ﺰاو‬‫اﻟ‬ ‫ﺮدد‬‫اﻟﺘ‬ ‫ﻲ‬‫ﻗﯿﻤﺘ‬‫ﻲ‬‫اﻟﺮﻧﯿﻨ‬ ‫ﺰاوي‬‫اﻟ‬ ‫ﺮدد‬‫اﻟﺘ‬ ‫ﺎﻧﺒﻲ‬‫ﺟ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ي‬)rω(‫ﺼﻒ‬ ‫ﻧ‬ ‫ﻰ‬‫إﻟ‬ ‫ﻄﺔ‬ ‫اﻟﻤﺘﻮﺳ‬ ‫ﺪرة‬‫اﻟﻘ‬ ‫ﺒﻂ‬ ‫ﺗﮭ‬ ‫ﺪﻣﺎ‬‫ﻋﻨ‬
‫اﻷﻋﻈﻢ‬ ‫ﻣﻘﺪارھﺎ‬.
‫اﻟﺬاﺗﻲ‬ ‫اﻟﺤﺚ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫اﻟﻰ‬ ‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﻧﺴﺒﺔ‬ ‫ھﻮ‬ ‫ﻛﺬﻟﻚ‬.‫ان‬ ‫أي‬:
11-‫ﻋﺎﻣﻞ‬‫اﻟﻨﻮﻋﯿﺔ‬)Qf: (‫ﻧﺴﺒﺔ‬ ‫ھﻮ‬‫اﻟﺮﻧﯿﻨﻲ‬ ‫اﻟﺰاوي‬ ‫اﻟﺘﺮدد‬)ωr(‫اﻟﻰ‬‫اﻟﺰاوي‬ ‫اﻟﺘﺮدد‬ ‫ﻧﻄﺎق‬)∆ω. (‫ﻣﻦ‬ ‫ﻣﺠﺮد‬ ‫ﻋﺪد‬ ‫وھﻮ‬
‫اﻟﻮﺣﺪات‬.‫ان‬ ‫أي‬:
‫س‬/‫اﻟﺮﻧﯿﻨﻲ‬ ‫اﻟﺘﺮدد‬ ‫ﻟﺤﺴﺎب‬ ‫رﯾﺎﺿﯿﺔ‬ ‫ﻋﻼﻗﺔ‬ ‫اﺷﺘﻖ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﻲ‬ ‫اﻟﺮﻧﯿﻦ‬ ‫ﺷﺮط‬ ‫ﻣﻦ‬.
‫ج‬/
CL2
1
f
LC4
1
f1LCf4
Cf2
1
Lf2XX
r
2
2
r
2
r
2
r
rCL
π
=∴
π
=⇒=π⇒
π
=π⇒=
‫س‬/‫ﻋﺎﻣﻞ‬ ‫ﻟﺤﺴﺎب‬ ‫رﯾﺎﺿﯿﺔ‬ ‫ﻋﻼﻗﺔ‬ ‫اﺷﺘﻖ‬‫اﻟﻨﻮﻋﯿﺔ‬.
‫ج‬/
C
L
R
1
CL
LL
R
1
CL
L
R
1
L
R
CL
1
Qf r
=
×
×=×==
ω∆
ω
=
C
L
R
1
QforQf r
=
ω∆
ω
=
L
R
=ω∆ )‫اﻟﻌﻮاﻣﻞ‬ ‫ﻣﻮﺟﺐ‬(
∆ω = ω2 – ω1

43. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-44-
‫ﺧﺎﺻﺔ‬ ‫ﺣﺎﻻت‬:
1-‫ﻓﺎن‬ ‫رﻧﯿﻦ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫ﻋﻠﻰ‬ ‫وﻣﺘﺴﻌﺔ‬ ‫وﻣﺤﺚ‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺗﺤﺘﻮي‬ ‫او‬ ‫ﺻﺮف‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺗﺤﺘﻮي‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬:
X=0 , Z=R , 0=φ
‫واﺣﺪ‬ ‫طﻮر‬ ‫ﻓﻲ‬ ‫واﻟﺘﯿﺎر‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ان‬ ‫أي‬.
2-‫ﻓﺎن‬ ‫ﺻﺮف‬ ‫ﻣﺤﺚ‬ ‫ﺗﺤﺘﻮي‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﯿﺎر‬ ‫داﺋﺮة‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬:
R=0 , Z=XL ,
2
π
=φ
‫طﻮر‬ ‫ﻓﺮق‬ ‫ﺑﺰاوﯾﺔ‬ ‫اﻟﺘﯿﺎر‬ ‫ﺗﺴﺒﻖ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ان‬ ‫أي‬90º.
3-‫ﻓﺎن‬ ‫ﺻﺮف‬ ‫ﻣﺘﺴﻌﺔ‬ ‫ﺗﺤﺘﻮي‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﯿﺎر‬ ‫داﺋﺮة‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬:
R=0 , Z=XC ,
2
π
−=φ
‫طﻮر‬ ‫ﻓﺮق‬ ‫ﺑﺰاوﯾﺔ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻋﻦ‬ ‫ﺗﺘﺨﻠﻒ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ان‬ ‫أي‬°90.
‫ﺛﺎﻧﻴﺎ‬:‫اﻟﺘﻮازي‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﻨﺎﺻﺮ‬ ‫رﺑﻂ‬:
•‫ﻟﻠﻔﻮﻟﻄﯿﺎت‬ ‫اﻟﻄﻮرﯾﺔ‬ ‫اﻟﻤﺘﺠﮭﺎت‬)VR , VL , VC(‫اﻻﺳﻨﺎد‬ ‫ﻣﺤﻮر‬ ‫ﻣﻦ‬ ‫اﻟﻤﻮﺟﺐ‬ ‫اﻻﺗﺠﺎه‬ ‫ﻋﻠﻰ‬ ‫ﺗﻨﻄﺒﻖ‬)‫اﻟﻤﺤﻮر‬x.(
•‫ﻟﻠﺘﯿﺎرات‬ ‫اﻟﻄﻮرﯾﺔ‬ ‫اﻟﻤﺘﺠﮭﺎت‬)IR , IL , IC(‫طﻮر‬ ‫ﻓﺮق‬ ‫زاوﯾﺔ‬ ‫ﻣﻨﮭﺎ‬ ‫ﻛﻞ‬ ‫ﯾﺼﻨﻊ‬φ‫اﻟﻤﺤﻮر‬ ‫ﻣﻊ‬x.
‫ﺍﻟ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﻌﻨﺎﺻﺮ‬ ‫ﺭﺑﻂ‬ ‫ﺧﻮﺍﺹ‬‫ﺘﻮﺍﺯﻱ‬:
1-‫ﺔ‬‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫ﻢ‬‫ﻧﺮﺳ‬ ‫ﺬﻟﻚ‬‫ﻟ‬ ‫ﻲ‬‫اﻟﻜﻠ‬ ‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﻓﺮق‬ ‫وﯾﺴﺎوي‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﺟﻤﯿﻊ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺘﺴﺎوي‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬ ‫ﻣﻘﺪار‬
‫اﻹﺳﻨﺎد‬ ‫ﻣﺤﻮر‬ ‫ﻋﻠﻰ‬)‫ﻛﺄﺳﺎس‬(‫ان‬ ‫أي‬:
‫ﺖ‬‫ﺑ‬‫ﺎ‬‫ﺛ‬VVVVV TCLR ====
2-‫ﺎر‬‫اﻟﺘﯿ‬ ‫ﺪار‬‫ﻣﻘ‬‫ﺬﻟﻚ‬ ‫ﻟ‬ ‫ﺮ‬‫آﺧ‬ ‫ﻰ‬ ‫إﻟ‬ ‫ﺼﺮ‬‫ﻋﻨ‬ ‫ﻦ‬‫ﻣ‬ ‫ﻒ‬ ‫ﯾﺨﺘﻠ‬‫ﻲ‬ ‫اﻟﻜﻠ‬ ‫ﺎر‬‫اﻟﺘﯿ‬ ‫ﺴﺎب‬‫ﻟﺤ‬)‫ﺎر‬‫اﻟﺘﯿ‬‫ﺼﻞ‬‫اﻟﻤﺤ‬(‫ﺰه‬‫رﻣ‬ ‫ﺬي‬ ‫واﻟ‬)TI(‫ﻊ‬ ‫ﻧﺠﻤ‬
‫اﻟﺘﯿﺎرات‬‫طﻮرﯾﺎ‬ ‫ﺟﻤﻌﺎ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻟﻌﻨﺎﺻﺮ‬)‫اﺗﺠﺎھﯿﺎ‬(‫ﻖ‬‫ﺑﺘﻄﺒﯿ‬ ‫ﻚ‬‫وذﻟ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺔ‬‫زاوﯾ‬ ‫وﺟﻮد‬ ‫ﺑﺴﺒﺐ‬‫ﻦ‬‫ﻣ‬ ‫ﺎﻏﻮرس‬‫ﻓﯿﺜ‬ ‫ﺔ‬‫ﻣﺒﺮھﻨ‬
‫اﻟﺘﯿﺎر‬ ‫ﻣﺨﻄﻂ‬‫ادﻧﺎه‬:
‫ﻋﻨﺎﺻﺮ‬ ‫وﺣﺴﺐ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻣﺨﻄﻄﺎت‬
‫اﻟﺮﺑﻂ‬ ‫اﻟﻤﺘﻮازﯾﺔ‬ ‫اﻟﺪاﺋﺮة‬.

44. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-45-
‫وﺑﺘﻄ‬ ‫اﻋﻼه‬ ‫اﻟﻤﺨﻄﻄﺎت‬ ‫ﻣﻦ‬‫اﻟﻜﻠﻲ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻧﺠﺪ‬ ‫ﻓﯿﺜﺎﻏﻮرس‬ ‫ﻣﺒﺮھﻨﺔ‬ ‫ﺒﯿﻖ‬)TI(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻋﻨﺎﺻﺮ‬ ‫وﺣﺴﺐ‬:
‫ﺣﯿﺚ‬:
XI:‫وﯾﺴ‬ ‫اﻟﻤﺤﺼﻠﺔ‬ ‫اﻟﺮادة‬ ‫ﺗﯿﺎر‬‫ﺗﯿﺎر‬ ‫ﺑﯿﻦ‬ ‫اﻟﻔﺮق‬ ‫ﺎوي‬‫اﻟﺮادﺗﯿﻦ‬)‫اﻟﺴﻌﺔ‬ ‫ورادة‬ ‫اﻟﺤﺚ‬ ‫رادة‬‫ان‬ ‫أي‬:)LCX III −=(
‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫زاوﯾﺔ‬ ‫ﺣﺴﺎب‬ ‫ﯾﻤﻜﻦ‬ ‫ﻛﺬﻟﻚ‬)φ(‫اﻟﻜﻠﻲ‬ ‫اﻟﺘﯿﺎر‬ ‫ﺑﯿﻦ‬)‫اﻟﻤﺤﺼﻞ‬(‫واﻟﻔﻮﻟﻄﯿﺔ‬‫ﻣﻦ‬)φtan(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬:
‫اﻟﻘﺪرة‬ ‫ﻋﺎﻣﻞ‬ ‫ﻟﺤﺴﺎب‬ ‫اﻣﺎ‬)pf(‫ﻓﻨﺴﺘﺨﺪم‬)φcos(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬:
‫ﻟﺤﻈﺔ‬ ‫اﯾﺔ‬ ‫ﻓﻲ‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻻﯾﺠﺎد‬ ‫اﻣﺎ‬)‫اﻻﻧﻲ‬ ‫اﻟﻜﻠﻲ‬ ‫اﻟﺘﯿﺎر‬(‫واﻟﻔﻮﻟﻄﯿﺔ‬‫ﻲ‬‫ﻓ‬‫ﺔ‬‫ﻟﺤﻈ‬ ‫ﺔ‬‫اﯾ‬)‫ﺔ‬‫اﻟﻔﻮﻟﻄﯿ‬‫اﻻﻧﯿ‬‫ﺔ‬(‫ﺴﺘﺨﺪم‬‫ﻓﻨ‬‫ﺎدﻻت‬‫ﻣﻌ‬
‫واﻟﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﺘﯿﺎر‬‫اﻻﺗﯿﺔ‬:
‫ﺣﯿﺚ‬:
f2,V2V,I2I effmeffm π=ω==
‫اﻟﻤﺼﺪر‬ ‫ﻓﻮﻟﻄﯿﺔ‬ ‫ﺗﻤﺜﻞ‬ ‫اﻟﻤﺆﺛﺮة‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬)V(‫واﻟﺘﯿﺎر‬‫اﻟﻤﺤﺼﻞ‬ ‫اﻟﺘﯿﺎر‬ ‫ﯾﻤﺜﻞ‬ ‫اﻟﻤﺆﺛﺮ‬)TI(.
‫اﻟﺮﺑﻊ‬‫اﻟﺮاﺑﻊ‬)tsin(II
or
‫اﻟﺮﺑﻊ‬‫اﻻول‬)tsin(II
‫اﺳﺎس‬)tsin(VV
m)ins(T
m)ins(T
mins
φ−ω=
φ+ω=
ω=
2
L
2
R
2
T
2
C
2
R
2
T
2
X
2
R
2
T
2
LC
2
R
2
T
III
or
III
or
IIIor)II(II
+=
+=
+=−+=
R
Z
cospfor
I
I
cospf
T
R
=φ==φ=
)LR()CR()CLR(
I
I
tanor
I
I
tanor
I
II
tan
R
L
R
C
R
LC
−−−−
−
=φ=φ
−
=φ
‫ﻟﺪاﺋﺮة‬)R-L-C(‫ﻟﻠﺨﻮاص‬
‫اﻟﺤﺜﯿﺔ‬ ‫او‬ ‫اﻟﺴﻌﻮﯾﺔ‬.
‫ﻟﺪاﺋﺮة‬)R-C(
‫ﻟﺪاﺋﺮة‬)R-L(
‫داﺋﺮة‬)R-L-C(‫اﻟﺴﻌﻮﯾﺔ‬ ‫ﻟﻠﺨﻮاص‬‫داﺋﺮة‬ ‫او‬)R-C(
.
‫داﺋﺮة‬)R-L-C(‫اﻟﺤﺜﯿﺔ‬ ‫ﻟﻠﺨﻮاص‬‫داﺋﺮة‬ ‫او‬)R-L. (

45. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-46-
3-‫ﻟﻠﺪاﺋﺮة‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻤﻤﺎﻧﻌﺔ‬)Z(‫واﻟﻤﻘﺎوﻣﺔ‬)R(‫اﻟﺤﺚ‬ ‫ورادة‬)XL(‫اﻟﺴﻌﺔ‬ ‫ورادة‬)XC(‫ﺎﻧ‬‫ﻟﻘ‬ ‫ﺎ‬‫وﻓﻘ‬ ‫ﺴﺐ‬‫ﺗﺤ‬ ‫اﻟﺮﺑﻂ‬ ‫ھﺬا‬ ‫ﻓﻲ‬‫ﻮن‬
‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اوم‬:
‫ﻣﻼﺣﻈﺎت‬/
1-‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺧﻼل‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﻛﺎن‬ ‫اذا‬)IC(‫اﻟﻤﺤﺚ‬ ‫ﺧﻼل‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬)IL(‫ﺔ‬‫اﻟﻤﺘﻮازﯾ‬ ‫ﺪاﺋﺮة‬‫ﻟﻠ‬ ‫ﻓﺎن‬
‫اﻟﺮﺑﻂ‬:
•‫ﺧﻮاص‬‫اﻟﺪاﺋﺮة‬‫ﺳﻌﻮﯾﺔ‬‫اﻟﻤﺤﺼﻠﺔ‬ ‫اﻟﺮادة‬ ‫ﺗﯿﺎر‬ ‫وان‬)IX(‫ﻣﻮﺟﺐ‬
•‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫زاوﯾﺔ‬)φ(‫ﻲ‬‫اﻟﻜﻠ‬ ‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫ﺑﯿﻦ‬)IT(‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫وﻣﺘﺠ‬
‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬)V(‫ﻣﻮﺟﺒﺔ‬.
•‫اﻟﻜﻠﻲ‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬)IT(‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﯾﺴﺒﻖ‬)V(‫ﺮق‬‫ﻓ‬ ‫ﺑﺰاوﯾﺔ‬
‫طﻮر‬)φ. (
•‫اﻷول‬ ‫اﻟﺮﺑﻊ‬ ‫ﻓﻲ‬ ‫ﯾﺮﺳﻢ‬ ‫ﻟﻠﺘﯿﺎر‬ ‫ﻣﺜﻠﺚ‬)‫اﻻﻋﻠﻰ‬ ‫ﻧﺤﻮ‬(.
2-‫ﻮر‬ ‫اﻟﻄ‬ ‫ﮫ‬ ‫ﻣﺘﺠ‬ ‫ﺎن‬ ‫ﻛ‬ ‫اذا‬‫ﺴﻌﺔ‬ ‫اﻟﻤﺘ‬ ‫ﻼل‬ ‫ﺧ‬ ‫ﺎر‬ ‫ﻟﻠﺘﯿ‬)IC(‫ﺚ‬ ‫اﻟﻤﺤ‬ ‫ﻼل‬ ‫ﺧ‬ ‫ﺎر‬ ‫ﻟﻠﺘﯿ‬ ‫ﻮر‬ ‫اﻟﻄ‬ ‫ﮫ‬ ‫ﻣﺘﺠ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﻐﺮ‬ ‫اﺻ‬)IL(‫ﺪاﺋﺮة‬ ‫ﻟﻠ‬ ‫ﺎن‬ ‫ﻓ‬
‫اﻟﺮﺑﻂ‬ ‫اﻟﻤﺘﻮازﯾﺔ‬:
•‫ﺧﻮاص‬‫اﻟﺪاﺋﺮة‬‫ﺣﺜﯿﺔ‬‫اﻟﻤﺤﺼﻠﺔ‬ ‫اﻟﺮادة‬ ‫ﺗﯿﺎر‬ ‫وان‬)IX(‫ﺳﺎﻟﺐ‬
•‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫زاوﯾﺔ‬)φ(‫ﻲ‬‫اﻟﻜﻠ‬ ‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﻣﺘﺠﮫ‬ ‫ﺑﯿﻦ‬)IT(‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫وﻣﺘﺠ‬
‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬)V(‫ﺳﺎﻟﺒﺔ‬
•‫ﻟﻠ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬‫ﺘ‬‫اﻟﻜﻠﻲ‬ ‫ﯿﺎر‬)IT(‫ﯾﺘﺄﺧﺮ‬‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﻋﻦ‬)V(‫ﺔ‬‫ﺑﺰاوﯾ‬
‫طﻮر‬ ‫ﻓﺮق‬)φ. (
•‫اﻟﺮاﺑﻊ‬ ‫اﻟﺮﺑﻊ‬ ‫ﻓﻲ‬ ‫ﯾﺮﺳﻢ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻣﺜﻠﺚ‬)‫ﻧﺤﻮ‬‫اﻷﺳﻔﻞ‬(.
3-‫اﻟﻤﺘﺴﻌﺔ‬ ‫ﺧﻼل‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﻛﺎن‬ ‫اذا‬)IC(‫اﻟﻤﺤﺚ‬ ‫ﺧﻼل‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﯾﺴﺎوي‬)IL(‫ﻟﻠﺪا‬ ‫ﻓﺎن‬‫اﻟﻤﺘﻮازﯾﺔ‬ ‫ﺋﺮة‬
‫اﻟﺮﺑﻂ‬:
•‫اﻟﻤﺤﺼﻠﺔ‬ ‫اﻟﺮادة‬ ‫ﺗﯿﺎر‬ ‫وان‬ ‫ﺻﺮف‬ ‫اوﻣﯿﺔ‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺧﻮاص‬)IX=0(
•‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫زاوﯾﺔ‬ ‫ﺗﻜﻮن‬)φ(‫اﻟﻜﻠﻲ‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﺑﯿﻦ‬)IT(‫وﻣﺘﺠﮫ‬
‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬)V(‫ﺻﻔﺮ‬.
•‫ﻟﻠ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬‫ﺘ‬‫اﻟﻜﻠﻲ‬ ‫ﯿﺎر‬)IT(‫ﻋﻠﻰ‬ ‫ﯾﻨﻄﺒﻖ‬‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬V)‫أي‬
‫اﻧﮭﻤﺎ‬‫واﺣﺪ‬ ‫طﻮر‬ ‫ﻓﻲ‬(.
C
C
L
L
RT I
V
X,
I
V
X,
I
V
R,
I
V
Z ====

46. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-47-
‫س‬/‫ان‬ ‫اﺛﺒﺖ‬ ‫اﻟﺘﻮازي‬ ‫رﺑﻂ‬ ‫ﻓﻲ‬:
R
Z
cospf =φ=
‫ج‬/
R
Z
V
Z
.
R
V
Z
V
R
V
cospf
Z
V
I,
R
V
I
I
I
cospf
TR
T
R
===φ=∴
==
=φ=
Q
‫ﺍﳌﺘﻨﺎﻭﺏ‬ ‫ﺍﻟﺘﻴﺎﺭ‬ ‫ﺩﺍﺋﺮﺓ‬ ‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬:-
‫ﹰ‬‫ﻻ‬‫ﺃﻭ‬:-‫ﺻﺮﻑ‬ ‫ﻣﻘﺎﻭﻣﺔ‬ ‫ﻣﺜﻞ‬ ‫ﻭﺍﺣﺪ‬ ‫ﻋﻨﺼﺮ‬ ‫ﲢﺘﻮﻱ‬)R(‫ﺻﺮﻑ‬ ‫ﳏﺚ‬ ‫ﺍﻭ‬)L(‫ﻣﺘﺴﻌﺔ‬ ‫ﺍﻭ‬‫ﺻﺮﻑ‬ ‫ﺳﻌﺔ‬ ‫ﺫﺍﺕ‬)C(‫ﻓﺎﻥ‬
‫ﺍﻟ‬ ‫ﺑﺎﻟﻌﻼﻗﺎﺕ‬ ‫ﺗﻌﻄﻰ‬ ‫ﻭﺍﻟﺘﻴﺎﺭ‬ ‫ﺍﻟﻔﻮﻟﻄﻴﺔ‬ ‫ﻣﻌﺎﺩﻻﺕ‬‫ﺘﺎﻟﻴﺔ‬:
‫ﺍﻟﺼﺮﻑ‬ ‫ﺍﳌﻘﺎﻭﻣﺔ‬ ‫ﰲ‬:
)t(SinVV mR
ω=
)t(SinII mR
ω=
‫ﺍﻟﺼﺮﻑ‬ ‫ﺍﶈﺚ‬ ‫ﰲ‬:
)90t(SinVV mL
°+ω=
)t(SinII mL
ω=
‫او‬
)t(SinVV mL
ω=
)90t(SinII mL
°−ω=
‫ﰲ‬‫ﺍﻟﺼﺮﻑ‬ ‫ﺍﻟﺴﻌﺔ‬ ‫ﺫﺍﺕ‬ ‫ﺍﳌﺘﺴﻌﺔ‬:
)t(SinVV mC
ω=
)90t(SinII mC
°+ω=
‫او‬
)90t(SinVV mC
°−ω=
)t(SinII mC
ω=
‫ﺗﺬﻛﺮ‬
‫ﻮر‬‫اﻟﻄ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺔ‬‫زاوﯾ‬ ‫ان‬ ‫أي‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻨﻄﺒﻖ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬
‫ا‬ ‫ﻣﺘﺠﮫ‬ ‫ﺑﯿﻦ‬‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫وﻣﺘﺠﮫ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫ﻟﻄﻮر‬)0=φ. (
‫ﺴﺎوي‬‫ﺗ‬ ‫ﻮر‬‫ط‬ ‫ﺮق‬‫ﻓ‬ ‫ﺔ‬‫ﺑﺰاوﯾ‬ ‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﯾﺴﺒﻖ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬90º
)°=φ 90. (
‫ﺴﺎوي‬‫ﺗ‬ ‫ﻮر‬‫ط‬ ‫ﺮق‬‫ﻓ‬ ‫ﺔ‬‫ﺑﺰاوﯾ‬ ‫ﺔ‬‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﻣﺘﺠﮫ‬ ‫ﻋﻦ‬ ‫ﯾﺘﺄﺧﺮ‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬
90º)°=φ 90. (
‫ﺴﺎوي‬‫ﺗ‬ ‫ﻮر‬‫ط‬ ‫ﺮق‬‫ﻓ‬ ‫ﺔ‬‫ﺑﺰاوﯾ‬ ‫ﺔ‬‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﯾﺴﺒﻖ‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬90º
)°=φ 90. (
‫ﺴﺎوي‬‫ﺗ‬ ‫ﻮر‬‫ط‬ ‫ﺮق‬‫ﻓ‬ ‫ﺔ‬‫ﺑﺰاوﯾ‬ ‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﻣﺘﺠﮫ‬ ‫ﻋﻦ‬ ‫ﯾﺘﺄﺧﺮ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬
90º)°=φ 90. (

47. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-48-
‫ﺛﺎﻧﻴﺎ‬:‫ﻋﻠﻰ‬ ‫ﻣﺮﺑﻮﻃﺔ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﺛﻼﺛﺔ‬ ‫ﺍﻭ‬ ‫ﻋﻨﺼﺮﻳﻦ‬ ‫ﻋﻠﻰ‬ ‫ﲢﺘﻮﻱ‬‫ﻣﺜﻞ‬ ‫ﺍﻟﺘﻮﺍﱄ‬)R-L(‫ﺍﻭ‬)R-C(‫ﺍﻭ‬)R-L-C(‫ﻓﺎﻥ‬
‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺎﺕ‬ ‫ﺗﻌﻄﻰ‬ ‫ﻭﺍﻟﺘﻴﺎﺭ‬ ‫ﺍﻟﻔﻮﻟﻄﻴﺔ‬ ‫ﻣﻌﺎﺩﻻﺕ‬:
)R-L(‫او‬)R-L-C(‫اﻟﺤﺜﯿﺔ‬ ‫اﻟﺨﻮاص‬ ‫ﻓﻲ‬.
)t(SinII
)t(SinVV
m
mT
ω=
φ+ω=
)R-C(‫او‬)R-L-C(‫اﻟﺴﻌﻮﯾﺔ‬ ‫اﻟﺨﻮاص‬ ‫ﻓﻲ‬.
)t(SinII
)t(SinVV
m
mT
ω=
φ−ω=
)R-L-C(‫إذا‬‫ﻛﺎﻧﺖ‬
‫ﺻﺮف‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺧﻮاص‬ ‫اﻟﺪاﺋﺮة‬ ‫ﺧﻮاص‬)‫اوﻣﯿﺔ‬. (
)t(SinII
)t(SinVV
m
mT
ω=
ω=
‫ﺛﺎﻧﻴﺎ‬:‫ﻣﺜـﻞ‬ ‫ﺍﻟﺘﻮﺍﺯﻱ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺮﺑﻮﻃﺔ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﺛﻼﺛﺔ‬ ‫ﺍﻭ‬ ‫ﻋﻨﺼﺮﻳﻦ‬ ‫ﻋﻠﻰ‬ ‫ﲢﺘﻮﻱ‬)R-C(‫ﺍﻭ‬)R-L(‫ﺍﻭ‬)R-L-C(
‫ﺗﻌﻄ‬ ‫ﻭﺍﻟﺘﻴﺎﺭ‬ ‫ﺍﻟﻔﻮﻟﻄﻴﺔ‬ ‫ﻣﻌﺎﺩﻻﺕ‬ ‫ﻓﺎﻥ‬‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺎﺕ‬ ‫ﻰ‬:
)R-C(‫او‬)R-L-C(‫اﻟﺴﻌﻮﯾﺔ‬ ‫اﻟﺨﻮاص‬ ‫ﻓﻲ‬.
)90t(SinII
)t(SinVV
mT
m
°+ω=
ω=
)R-L(‫او‬)R-L-C(‫اﻟﺤﺜﯿﺔ‬ ‫اﻟﺨﻮاص‬ ‫ﻓﻲ‬.
)t(SinII
)t(SinVV
mT
m
φ−ω=
ω=
)R-L-C(‫ﺧﻮاص‬ ‫ﻛﺎﻧﺖ‬ ‫إذا‬‫ﺻﺮف‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺧﻮاص‬ ‫اﻟﺪاﺋﺮة‬)‫اوﻣﯿﺔ‬. (
‫ﻣﺘﺠ‬ ‫ﯾﺴﺒﻖ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬‫ﺴﺎوي‬‫ﺗ‬ ‫ﻮر‬‫ط‬ ‫ﻓﺮق‬ ‫ﺑﺰاوﯾﺔ‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫ﮫ‬
φ‫ﻣﻮﺟﺒﺔ‬.
‫ﻮر‬‫ط‬ ‫ﺮق‬‫ﻓ‬ ‫ﺔ‬‫ﺑﺰاوﯾ‬ ‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫ﻦ‬‫ﻋ‬ ‫ﺄﺧﺮ‬‫ﯾﺘ‬ ‫ﺔ‬‫اﻟﻜﻠﯿ‬ ‫ﺔ‬‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬
‫ﺗﺴﺎوي‬φ‫ﺳﺎﻟﺒﺔ‬.
‫ﺮق‬‫ﻓ‬ ‫ﺔ‬‫زاوﯾ‬ ‫ان‬ ‫أي‬ ‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻨﻄﺒﻖ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬
‫ا‬‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ ‫ﺑﯿﻨﮭﻤﺎ‬ ‫ﻟﻄﻮر‬)0=φ. (
‫ﺴﺎوي‬‫ﺗ‬ ‫ﻮر‬‫ط‬ ‫ﺮق‬‫ﻓ‬ ‫ﺑﺰاوﯾﺔ‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬ ‫ﯾﺴﺒﻖ‬ ‫اﻟﻜﻠﻲ‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬
φ‫ﻣﻮﺟﺒﺔ‬.
‫ﻮر‬‫ط‬ ‫ﺮق‬‫ﻓ‬ ‫ﺔ‬‫ﺑﺰاوﯾ‬ ‫ﺔ‬‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫ﻦ‬‫ﻋ‬ ‫ﺄﺧﺮ‬‫ﯾﺘ‬ ‫ﻲ‬‫اﻟﻜﻠ‬ ‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬
‫ﺗﺴﺎوي‬φ‫ﺳ‬‫ﺎﻟﺒﺔ‬.
)t(SinII
)t(SinVV
m
mT
ω=
ω=
‫ﺮق‬‫ﻓ‬ ‫ﺔ‬‫زاوﯾ‬ ‫ان‬ ‫أي‬ ‫ﺔ‬‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫ﻮر‬‫اﻟﻄ‬ ‫ﮫ‬‫ﻣﺘﺠ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﯾﻨﻄﺒﻖ‬ ‫اﻟﻜﻠﻲ‬ ‫ﻟﻠﺘﯿﺎر‬ ‫اﻟﻄﻮر‬ ‫ﻣﺘﺠﮫ‬
‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ ‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﻄﻮر‬)0=φ. (

48. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-49-
1-‫ﯾﻮﺟﺪ‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫رﺑﻂ‬ ‫ﻓﻲ‬
‫ﺔ‬‫ﻟﻠﻔﻮﻟﻄﯿ‬ ‫ﺪھﻤﺎ‬‫اﺣ‬ ‫ﻣﺨﻄﻄﺎن‬‫ﺮ‬‫واﻵﺧ‬‫ﺎر‬‫ﻟﻠﺘﯿ‬ ‫ﻂ‬‫ﻣﺨﻄ‬ ‫ﻚ‬‫ھﻨﺎﻟ‬ ‫ﯿﺲ‬‫وﻟ‬ ‫ﺔ‬‫ﻟﻠﻤﻤﺎﻧﻌ‬‫ﺖ‬‫ﺛﺎﺑ‬ ‫ﺎر‬‫اﻟﺘﯿ‬ ‫ﻻن‬‫ﺪ‬‫ﻓﯿﻮﺟ‬ ‫ﻮازي‬‫اﻟﺘ‬ ‫ﻂ‬‫رﺑ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺎ‬‫اﻣ‬
‫ﻟﻠﻤﻤﺎ‬ ‫ﻣﺨﻄﻂ‬ ‫او‬ ‫ﻟﻠﻔﻮﻟﻄﯿﺔ‬ ‫ﻣﺨﻄﻂ‬ ‫ﯾﻮﺟﺪ‬ ‫وﻻ‬ ‫ﻓﻘﻂ‬ ‫ﻟﻠﺘﯿﺎر‬ ‫ﻣﺨﻄﻂ‬‫ﻧﻌﺔ‬.
2-‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اوم‬ ‫ﻗﺎﻧﻮن‬ ‫ﺗﻄﺒﯿﻖ‬ ‫ﯾﻤﻜﻦ‬ ‫اﻟﺘﻮازي‬ ‫او‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫رﺑﻂ‬ ‫ﻓﻲ‬:
C
C
C
L
L
L
R
R
T
T
I
V
X,
I
V
X,
I
V
R,
I
V
Z ====
3-‫اﻟﻤﻤﺎﻧﻌﺔ‬ ‫ﺗﺤﺴﺐ‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫رﺑﻂ‬ ‫ﻓﻲ‬‫اﻟﻜﻠﯿﺔ‬‫ﺔ‬‫اﻟﻤﻤﺎﻧﻌ‬ ‫ﻣﺜﻠﺚ‬ ‫ﻣﻦ‬ ‫اﻣﺎ‬)‫ﺎﻏﻮرس‬‫ﻓﯿﺜ‬ ‫ﺔ‬‫ﻣﺒﺮھﻨ‬(‫اوم‬ ‫ﺎﻧﻮن‬‫ﻗ‬ ‫ﻦ‬‫ﻣ‬ ‫او‬)
I
V
Z T
=(
‫ﺪرة‬‫اﻟﻘ‬ ‫ﻞ‬‫ﻋﺎﻣ‬ ‫ﻦ‬‫ﻣ‬ ‫او‬)
Z
R
cosPf =φ=(‫ﺔ‬‫اﻟﻈﺎھﺮﯾ‬ ‫ﺪرة‬‫اﻟﻘ‬ ‫ﻦ‬‫ﻣ‬ ‫او‬)ZIP 2
app =(‫ﺴﺐ‬ ‫ﻓﺘﺤ‬ ‫ﻮازي‬‫اﻟﺘ‬ ‫ﻂ‬‫رﺑ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺎ‬‫اﻣ‬ ،
‫ﺔ‬ ‫اﻟﻤﻤﺎﻧﻌ‬‫ﺔ‬ ‫اﻟﻜﻠﯿ‬‫اوم‬ ‫ﺎﻧﻮن‬ ‫ﻟﻘ‬ ‫ﺎ‬ ‫وﻓﻘ‬)
T
I
V
Z =(‫ﺪرة‬ ‫اﻟﻘ‬ ‫ﻞ‬ ‫ﻋﺎﻣ‬ ‫ﻦ‬ ‫ﻣ‬ ‫او‬)
R
Z
cosPf =φ=(‫ﺔ‬ ‫اﻟﻈﺎھﺮﯾ‬ ‫ﺪرة‬ ‫اﻟﻘ‬ ‫ﻦ‬ ‫ﻣ‬ ‫او‬
)Z.IP 2
Tapp =(.
4-‫اﻟﺘﻮازي‬ ‫او‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫رﺑﻂ‬ ‫ﻓﻲ‬‫اﻟﺤﺚ‬ ‫رادة‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﻓﺎن‬)LX(‫اﻟﺴﻌﺔ‬ ‫رادة‬ ‫او‬)CX(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اﻟﻌﻮاﻣﻞ‬ ‫ﺑﻤﻮﺟﺐ‬ ‫ﺗﺤﺴﺐ‬:
Cf2
1
Xor
C
1
X,Lf2XorLX CCLL
π
=
ω
=π=ω=
5-‫ﺑﻄﺎرﯾﺔ‬ ‫إﻟﻰ‬ ‫ﻣﻠﻒ‬ ‫رﺑﻂ‬ ‫اذا‬)‫ﻣﺴﺘﻤﺮ‬ ‫ﻣﺼﺪر‬(‫ﻔﺮ‬‫ﺻ‬ ‫ﺴﺎوي‬‫ﺗ‬ ‫ﮫ‬‫ﻟ‬ ‫ﺚ‬‫اﻟﺤ‬ ‫رادة‬ ‫ﻻن‬ ‫ﻼﻛﮫ‬‫اﺳ‬ ‫ﺔ‬‫ﻣﻘﺎوﻣ‬ ‫وھﻲ‬ ‫ﻓﻘﻂ‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﯾﻌﺘﺒﺮ‬
)XL= 0(‫ان‬ ‫ﺣﯿﺚ‬‫ﺻﻔﺮ‬ ‫ﯾﺴﺎوي‬ ‫اﻟﻤﺴﺘﻤﺮ‬ ‫اﻟﺘﯿﺎر‬ ‫ﺗﺮدد‬)f=0(‫ﺼﺮﯾﻦ‬‫ﻋﻨ‬ ‫ﻞ‬‫ﻓﯿﻌﻤ‬ ‫ﺎوب‬‫ﻣﺘﻨ‬ ‫ﺼﺪر‬‫ﻣ‬ ‫ﻰ‬‫إﻟ‬ ‫ﻒ‬‫اﻟﻤﻠ‬ ‫ﻂ‬‫رﺑ‬ ‫اذا‬ ‫ﺎ‬‫اﻣ‬
‫ھﻤﺎ‬‫ﻣﻘﺎوﻣﺔ‬)R(‫ﺣﺚ‬ ‫ورادة‬)XL. (
6-‫ﻛﻠﻤﺔ‬ ‫وردت‬ ‫اذا‬)‫ﻣﻠﻒ‬(‫ﺔ‬‫ﻛﻠﻤ‬ ‫وردت‬ ‫اذا‬ ‫ﺎ‬‫اﻣ‬ ‫ﺔ‬‫ﺣﺜﯿ‬ ‫ورادة‬ ‫ﺔ‬‫ﻣﻘﺎوﻣ‬ ‫ﻮد‬‫وﺟ‬ ‫ﻲ‬‫ﯾﻌﻨ‬ ‫ﺬا‬‫ﻓﮭ‬ ‫ﺎوب‬‫اﻟﻤﺘﻨ‬ ‫اﻟﺘﯿﺎر‬ ‫ﻟﺪواﺋﺮ‬ ‫اﻟﺴﺆال‬ ‫ﻓﻲ‬
)‫ﻣﺤﺚ‬(‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﻣﮭﻞ‬ ‫ﻣﻠﻒ‬ ‫ﺗﻌﻨﻲ‬ ‫ﻓﮭﻲ‬)R=0. (
7-‫ﻌﻮﯾﺔ‬‫ﺳ‬ ‫ﺪاﺋﺮة‬‫اﻟ‬ ‫ﻮاص‬‫ﺧ‬ ‫ﻮن‬‫وﺗﻜ‬ ‫اﻟﺴﻌﺔ‬ ‫رادة‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫اﻟﺤﺚ‬ ‫رادة‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬ ‫ﺣﺜﯿﺔ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﺧﻮاص‬ ‫ﺗﻜﻮن‬ ‫اﻟﺘﻮاﻟﻲ‬ ‫رﺑﻂ‬ ‫ﻓﻲ‬
‫اﻟﺤﺚ‬ ‫رادة‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫اﻟﺴﻌﺔ‬ ‫رادة‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬‫ﺮ‬‫اﻛﺒ‬ ‫ﺴﻌﺔ‬‫اﻟ‬ ‫رادة‬ ‫ﺖ‬‫ﻛﺎﻧ‬ ‫اذا‬ ‫ﺔ‬‫ﺣﺜﯿ‬ ‫ﺪاﺋﺮة‬‫اﻟ‬ ‫ﻮاص‬‫ﺧ‬ ‫ﻮن‬‫ﺗﻜ‬ ‫ﻮازي‬‫اﻟﺘ‬ ‫رﺑﻂ‬ ‫ﻓﻲ‬ ‫ﺑﯿﻨﻤﺎ‬
‫ا‬ ‫ﺳﻌﻮﯾﺔ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﺧﻮاص‬ ‫وﺗﻜﻮن‬ ‫اﻟﺤﺚ‬ ‫رادة‬ ‫ﻣﻦ‬‫اﻟﺴﻌﺔ‬ ‫رادة‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫اﻟﺤﺚ‬ ‫رادة‬ ‫ﻛﺎﻧﺖ‬ ‫ذا‬.
8-‫اﻟﺼﺤﯿﺢ‬ ‫اﻟﻮاﺣﺪ‬ ‫ھﻲ‬ ‫اﻟﻘﺪرة‬ ‫ﻟﻌﺎﻣﻞ‬ ‫ﻗﯿﻤﺔ‬ ‫اﻛﺒﺮ‬ ‫ان‬)‫ﻋ‬‫او‬ ‫ﺻﺮف‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫اﻟﺤﻤﻞ‬ ‫ﯾﻜﻮن‬ ‫ﻨﺪﻣﺎ‬‫اﻟ‬‫ﺪاﺋﺮة‬‫ﺔ‬‫ﺣﺎﻟ‬ ‫ﻓﻲ‬‫ﯿﻦ‬‫رﻧ‬(‫ﻞ‬‫واﻗ‬
‫اﻟﺼﻔﺮ‬ ‫ھﻲ‬ ‫ﻟﮫ‬ ‫ﻗﯿﻤﺔ‬)‫ﺮف‬‫ﺻ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ذات‬ ‫ﺴﻌﺔ‬‫ﻣﺘ‬ ‫او‬ ‫ﺻﺮف‬ ‫ﻣﺤﺚ‬ ‫اﻟﺤﻤﻞ‬ ‫ﯾﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬(‫ﻞ‬‫واﻗ‬ ‫ﻔﺮ‬‫ﺻ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺮ‬‫اﻛﺒ‬ ‫ﮫ‬‫ﻗﯿﻤﺘ‬ ‫ﻮن‬‫وﺗﻜ‬
‫اﻟﺼﺤﯿﺢ‬ ‫اﻟﻮاﺣﺪ‬ ‫ﻣﻦ‬‫ھﻲ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬)RL(‫او‬)RC(‫او‬)RLC(‫ﺗﻮازي‬ ‫او‬ ‫ﺗﻮاﻟﻲ‬.
‫ﺧﻼﺻﺔ‬

49. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-50-
‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﻔﺼﻞ‬ ‫ﻗﻮاﻧﻴﻦ‬
‫واﺣﺪ‬ ‫ﻋﻨﺼﺮ‬ ‫ﺗﺤﺘﻮي‬ ‫اﻟﺘﻲ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻗﻮاﻧﻴﻦ‬:
‫اوﻻ‬:‫ﺻﺮف‬ ‫ﻣﻘﺎوﻣﺔ‬
RIPorVIPorRI
2
1
PorVI
2
1
P
P
2
1
P
RIPorVIP
RIPorVIP
I
V
Ror
I
V
Ror
I
V
R
RZ,0X,0X
V2V,I2I,
)tsin(VV
)tsin(II
1cosPf,0
2
effaveffeffav
2
mavmmav
mav
2
RinsRRins
2
mmmmm
eff
eff
m
m
R
R
CL
effmeffm
mR
mR
====∴
=
==
==
===
===
==


ω=
ω=
=φ==φ
‫ﺛﺎﻧﻴﺎ‬:‫ﺻﺮف‬ ‫ﻣﺤﺚ‬)‫اﻟﻤﻘﺎوﻣﺔ‬ ‫ﻣﻬﻤﻞ‬ ‫ﻣﻠﻒ‬(
f2,
I
V
XorLX
XZ,0X,0R
)90tsin(II
)tsin(VV
or
)90tsin(VV
)tsin(II
0cosPf,90
L
L
LL
LC
mL
mL
mL
mL
π=ω=ω=
===



°−ω=
ω=



°+ω=
ω=
=φ=°=φ
‫ﺛﺎﻟﺜﺎ‬:‫ﺻﺮ‬ ‫ﺳﻌﺔ‬ ‫ذات‬ ‫ﻣﺘﺴﻌﺔ‬‫ف‬
f2,
I
V
Xor
C
1
X
XZ,0X,0R
)90tsin(VV
)tsin(II
or
)90tsin(II
)tsin(VV
0cosPf,90
C
C
CC
CL
mC
mC
mC
mC
π=ω=
ω
=
===



°−ω=
ω=



°+ω=
ω=
=φ=°=φ

50. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-51-
‫ﻋﻨﺎﺻﺮ‬ ‫ﺛﻼﺛﺔ‬ ‫او‬ ‫ﻋﻨﺼﺮﻳﻦ‬ ‫ﺗﺤﺘﻮي‬ ‫اﻟﺘﻲ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻗﻮاﻧﻴﻦ‬:
‫اﻟﺘﻮاﻟﻲ‬ ‫ﻗﻮاﻧﻴﻦ‬:
IIIII CLRT ====
‫اوﻻ‬:‫ﻧﺠﺪ‬ ‫اﻟﻔﻮﻟﻄﻴﺔ‬ ‫ﻣﺨﻄﻂ‬ ‫ﻣﻦ‬:
II,VV,V2V,I2I
)tsin(VVor)tsin(VV
)tsin(II
V
V
cosPf
V
V
tanor
V
V
tanor
V
VV
tan
VVVorVVVor)VV(VV
effTeffeffmeffm
m)ins(Tm)ins(T
mins
T
R
R
C
R
L
R
CL
2
C
2
R
2
T
2
L
2
R
2
T
2
CL
2
R
2
T
====
φ−ω=φ+ω=
ω=
=φ=
−
=φ=φ
−
=φ
+=+=−+=
‫ﺛﺎﻧﻴﺎ‬:‫ﻧﺠﺪ‬ ‫اﻟﻤﻤﺎﻧﻌﺔ‬ ‫ﻣﺨﻄﻂ‬ ‫ﻣﻦ‬:
Z
R
cosPf
R
X
tanor
R
X
tanor
R
XX
tan
XRZorXRZor)XX(RZ
CLCL
2
C
222
L
222
CL
22
=φ=
−
=φ=φ
−
=φ
+=+=−+=
‫اﻟﺘﻮازي‬ ‫ﻗﻮاﻧﻴﻦ‬:
VVVVV LCRT ====
‫ﻣﺨ‬ ‫ﻣﻦ‬‫ﻧﺠﺪ‬ ‫اﻟﺘﻴﺎر‬ ‫ﻄﻂ‬:
Teffeffeffmeffm
m)ins(Tm)ins(T
mins
T
R
R
L
R
C
R
LC
2
L
2
R
2
T
2
C
2
R
2
T
2
LC
2
R
2
T
II,VV,I2I,V2V
)tsin(IIor)tsin(II
)tsin(VV
R
Z
cosPfor
I
I
cosPf
I
I
tanor
I
I
tanor
I
II
tan
IIIorIIIor)II(II
====
φ−ω=φ+ω=
ω=
=φ==φ=
−
=φ=φ
−
=φ
+=+=−+=

51. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎﻟﺚ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻤﺘﻨﺎوب‬ ‫اﻟﺘﻴﺎر‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-52-
‫واﻟﺘﻮازي‬ ‫ﻟﻠﺘﻮاﻟﻲ‬ ‫ﻋﺎﻣﺔ‬ ‫ﻗﻮاﻧﻴﻦ‬:
‫اوﻻ‬:‫اوم‬ ‫ﻗﺎﻧﻮن‬
C
C
C
L
L
L
R
R
T
T
I
V
X,
I
V
X,
I
V
R,
I
V
Z ====
‫ﺛﺎﻧﻴﺎ‬:‫اﻟﻌﻮاﻣﻞ‬ ‫ﻣﻦ‬ ‫اﻟﺴﻌﺔ‬ ‫ورادة‬ ‫اﻟﺤﺚ‬ ‫رادة‬ ‫ﺣﺴﺎب‬
f2,
C
1
X,LX CL π=ω
ω
=ω=
‫ﺛﺎﻟﺜﺎ‬:‫اﻟﺘﻌﺮﻳﻒ‬ ‫ﻣﻦ‬ ‫اﻟﻘﺪرة‬ ‫ﻋﺎﻣﻞ‬ ‫ﺣﺴﺎب‬
app
real
P
P
Pf =
‫راﺑﻌ‬‫ﺎ‬:‫اﻟﻈﺎﻫﺮﻳﺔ‬ ‫واﻟﻘﺪرة‬ ‫اﻟﺤﻘﻴﻘﻴﺔ‬ ‫اﻟﻘﺪرة‬ ‫ﺣﺴﺎب‬
φ
===
φ===
cos
P
PorZIPorVIP
cosVIPorRIPorVIP
real
app
2
TappTTapp
TTreal
2
RrealRRreal
‫اﻟﺘﻮاﻟﻲ‬ ‫رﻧﻴﻦ‬ ‫ﻗﻮاﻧﻴﻦ‬:
C
C
C
r
L
Lrr
r
CrL
r
12
rr
T
r
appreal
CLRTCLX
I
V
X,
I
V
X,f2,
C
1
X,LX
C
L
R
1
QforQf
L
R
or
f2,
CL
1
,
CL2
1
f,
R
V
I
PP,1cosPf,0
RZ,XX,0X,VV,VV,0V
==π=ω
ω
=ω=
=
ω∆
ω
=
=ω∆ω−ω=ω∆
π=ω=ω
π
==
==φ==φ
======

52. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺮاﺑﻊ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻴﺔ‬ ‫اﻟﻤﻮﺟﺎت‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-53-
‫واﻟﺘﺴﻠﻢ‬ ‫اﻻرﺳﺎل‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ان‬‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻴﺔ‬ ‫ﻟﻠﻤﻮﺟﺎت‬‫ﻫﻤﺎ‬ ‫اﺳﺎﺳﻴﻴﻦ‬ ‫ﺟﻬﺎزﻳﻦ‬ ‫ﻋﻠﻰ‬ ‫ﺗﻌﺘﻤﺪ‬:
1-‫اﻟﻜﮭﺮوﻣﻐﻨﺎطﯿﺴﻲ‬ ‫اﻻھﺘﺰاز‬ ‫داﺋﺮة‬.2-‫اﻟﮭﻮاﺋﻲ‬.
‫اوﻻ‬:‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻲ‬ ‫اﻻﻫﺘﺰاز‬ ‫داﺋﺮة‬ ‫ﻗﻮاﻧﻴﻦ‬:
‫ان‬‫اﻟ‬‫ﺘﺮدد‬‫ﺗﺮدد‬ ‫و‬ ‫اﻟﻤﻬﺘﺰة‬ ‫ﻟﻠﺪاﺋﺮة‬ ‫اﻟﺰاوي‬‫ا‬‫اﻟﻤﻬﺘﺰة‬ ‫ﻟﺪاﺋﺮة‬‫ﺑﺎ‬ ‫ﻋﻨﻬﻤﺎ‬ ‫ﻳﻌﺒﺮ‬‫اﻻﺗﻴﺔ‬ ‫ﻟﻌﻼﻗﺎت‬:
,
‫ﺣﯿﺚ‬:
‫ﺛﺎﻧﻴﺎ‬:‫اﻟﻬﻮاﺋﻲ‬ ‫ﻗﻮاﻧﻴﻦ‬:
‫ﻃﻮل‬ ‫ﺣﺴﺎب‬‫ﺳﻠﻚ‬‫اﻟﻬﻮاﺋﻲ‬)L:(
‫اﻟﻬﻮاﺋﻲ‬ ‫ﺳﻠﻚ‬ ‫ﻃﻮل‬ ‫ﺣﺴﺎب‬ ‫ﻳﻤﻜﻦ‬)L(‫ﺗﺮددﻫﺎ‬ ‫او‬ ‫اﻟﻤﺴﺘﻠﻤﺔ‬ ‫او‬ ‫اﻟﻤﺮﺳﻠﺔ‬ ‫اﻟﻤﻮﺟﺔ‬ ‫ﻃﻮل‬ ‫ﺑﻤﻌﺮﻓﺔ‬‫ﻳﻠﻲ‬ ‫وﻛﻤﺎ‬:
1-‫ﻃﻮﻟﻪ‬ ‫ﻓﺎن‬ ‫ﻣﺆرض‬ ‫ﻏﻴﺮ‬ ‫اﻟﻬﻮاﺋﻲ‬ ‫ﻳﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬‫ﻳﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اﻟﻤﻮﺟﺔ‬ ‫ﻃﻮل‬ ‫ﻧﺼﻒ‬ ‫ﻳﺴﺎوي‬:
2-‫ﻣﺆرض‬ ‫اﻟﻬﻮاﺋﻲ‬ ‫ﻳﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬)‫ﺑﺎﻷرض‬ ‫ﻣﺘﺼﻞ‬ ‫أﻗﻄﺎﺑﻪ‬ ‫اﺣﺪ‬(‫ﻳﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫ﻣﻮﺟﺔ‬ ‫ﻃﻮل‬ ‫رﺑﻊ‬ ‫ﻳﺴﺎوي‬ ‫ﻃﻮﻟﻪ‬ ‫ﻓﺎن‬:
‫اﻟﻤﺮ‬ ‫اﻟﻤﻮﺟﺔ‬ ‫ﻃﻮل‬ ‫ﻟﺤﺴﺎب‬ ‫اﻣﺎ‬‫او‬ ‫ﺳﻠﺔ‬‫اﻟ‬ ‫ﻧﺴﺘﺨﺪم‬ ‫اﻟﻤﺴﺘﻠﻤﺔ‬‫اﻟﻤﻮﺟﻴﺔ‬ ‫ﻤﻌﺎدﻟﺔ‬:
‫ﺣﯿﺚ‬:
c:‫وﻣﻘﺪارھﺎ‬ ‫اﻟﻔﺮاغ‬ ‫ﻓﻲ‬ ‫اﻟﻀﻮء‬ ‫ﺳﺮﻋﺔ‬)c = 3×108
m/s.(
f:‫ﺑﺎﻟﮭﯿﺮﺗﺰ‬ ‫وﯾﻘﺎس‬ ‫اﻟﻤﻮﺟﺔ‬ ‫ﺗﺮدد‬)Hz.(
‫ﺗﺬﻛﺮ‬:
‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫ﻋﻨﻬﺎ‬ ‫ﻳﻌﺒﺮ‬ ‫ﻋﺎﻣﺔ‬ ‫ﺑﺼﻮرة‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺑﺎن‬‫اﻻﺗﻴﺔ‬ ‫اﻟﺮﻳﺎﺿﻴﺔ‬:
‫اﻟﻀﻮء‬ ‫ﺳﺮﻋﺔ‬ ‫اﻣﺎ‬‫اﻟﻔﺮاغ‬ ‫ﻓﻲ‬‫اﻻﺗﻴﺔ‬ ‫اﻟﺮﻳﺎﺿﻴﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫ﻋﻨﻬﺎ‬ ‫ﻓﻴﻌﺒﺮ‬:
f2π=ω
CL
1
=ω
t
x
c =
t
x
=ν
f
c
=λ
4
L
λ
=
CL2
1
f
π
=
2
L
λ
=

53. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺮاﺑﻊ‬:‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬ ‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻴﺔ‬ ‫اﻟﻤﻮﺟﺎت‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-54-
‫اﻟﺮاﺑﻊ‬ ‫اﻟﻔﺼﻞ‬ ‫ﻗﻮاﻧﻴﻦ‬
t
x
c,
t
x
,fc,
4
,
2
f2,
CL
1
,
CL2
1
f rr
==νλ=
λ
=
λ
=
π=ω=ω
π
=
ll
‫ﺍﻟﻔﺼﻞ‬ ‫ﻭﺍﺟﺒﺎﺕ‬
‫ﻣﺜﺎل‬1/‫ﺎ‬‫طﻮﻟﮭ‬ ‫ﻛﮭﺮوﻣﻐﻨﺎطﯿﺴﯿﺔ‬ ‫ﻣﻮﺟﺔ‬ ‫ﺗﺒﺚ‬ ‫ﺗﻠﻔﺎز‬ ‫ﻣﺤﻄﺔ‬)1.5m(‫ﻊ‬‫ﻣ‬ ‫ﺴﺘﻌﻤﻞ‬‫اﻟﻤ‬ ‫ﻒ‬‫ﻟﻠﻤﻠ‬ ‫ﺬاﺗﻲ‬‫اﻟ‬ ‫ﺚ‬‫اﻟﺤ‬ ‫ﻞ‬‫ﻣﻌﺎﻣ‬ ‫ﺪار‬‫ﻣﻘ‬ ‫ﺎ‬‫ﻣ‬
‫ﺳﻌﺘﮭﺎ‬ ‫ﻣﺘﺴﻌﺔ‬)4pF(‫اﻟﻤﻮﺟﻲ‬ ‫اﻟﻄﻮل‬ ‫ھﺬا‬ ‫ﺗﺒﺚ‬ ‫رﻧﯿﻦ‬ ‫داﺋﺮة‬ ‫ﻟﺘﻜﻮﯾﻦ‬.)‫ج‬/H10156 9−
×(
‫ﻣﺜﺎل‬2/‫ﻌﺘﮭﺎ‬‫ﺳ‬ ‫ﺪار‬‫ﻣﻘ‬ ‫ﺮف‬‫ﺻ‬ ‫ﻌﺔ‬‫ﺳ‬ ‫ذات‬ ‫ﺴﻌﺔ‬‫ﻣﺘ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺎﻟﻒ‬‫ﺗﺘ‬ ‫ﻛﮭﺮوﻣﻐﻨﺎطﯿﺴﻲ‬ ‫اھﺘﺰاز‬ ‫داﺋﺮة‬)F
50
µ
π
(‫ﺮف‬‫ﺻ‬ ‫ﺚ‬‫وﻣﺤ‬
‫ﺣﺜ‬ ‫ﻣﻌﺎﻣﻞ‬‫اﻟﺬاﺗﻲ‬ ‫ﮫ‬)mH
5
π
(‫ﻣﻘﺪار‬ ‫اﺣﺴﺐ‬:
1-‫اﻟﺘﺮ‬‫اﻟﺪاﺋﺮة‬ ‫ﻟﮭﺬه‬ ‫اﻟﻄﺒﯿﻌﻲ‬ ‫دد‬.2-‫اﻟﺪاﺋﺮة‬ ‫ﻟﮭﺬه‬ ‫اﻟﺰاوي‬ ‫اﻟﺘﺮدد‬.)‫ج‬/1-1000Hz،2-6280rad/sec(
‫ﻣﺜﺎل‬3/‫ﺗﺮدده‬ ‫ﻣﺼﺪر‬ ‫ﯾﺸﻌﮭﺎ‬ ‫ﻛﮭﺮوﻣﻐﻨﺎطﯿﺴﯿﺔ‬ ‫ﻟﻤﻮﺟﺎت‬ ‫اﻟﻤﻮﺟﻲ‬ ‫اﻟﻄﻮل‬ ‫ﻣﺎ‬)(60Hz‫؟‬)‫ج‬/5×106
m. (
‫ﻣﺜﺎل‬4/‫طﻮ‬ ‫اﺣﺴﺐ‬‫ﺗﺮددھﺎ‬ ‫اﺷﺎرة‬ ‫ﻻﺳﺘﻘﺒﻞ‬ ‫واﻟﻼزم‬ ‫اﻟﮭﻮاﺋﻲ‬ ‫ﺳﻠﻚ‬ ‫ل‬)600MHz(‫اﻟﮭﻮاﺋﻲ‬ ‫ﻛﺎن‬ ‫اذا‬:
1-‫ﻣﺆرض‬ ‫ﻏﯿﺮ‬.2-‫ﻣﺆرض‬)‫ج‬/1-0.25m،2-0.125m. (
‫ﻣﺜﺎل‬5/‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻧﻔﺠﺎر‬ ‫وﻗﻊ‬)15km(‫؟‬ ‫ﻮﺗﮫ‬‫ﺻ‬ ‫ﻤﺎﻋﮫ‬‫وﺳ‬ ‫ﺎر‬‫ﻟﻼﻧﻔﺠ‬ ‫ﺪ‬‫اﻟﺮاﺻ‬ ‫ﺔ‬‫رؤﯾ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺔ‬‫اﻟﺰﻣﻨﯿ‬ ‫ﺮة‬‫اﻟﻔﺘ‬ ‫ﺎ‬‫ﻣ‬ ، ‫راﺻﺪ‬ ‫ﻣﻦ‬
)‫ﺳﺮﻋﺔ‬ ‫اﻋﺘﺒﺮ‬‫اﻟﺼﻮت‬340m/sec. ()‫ج‬/44.1176sec. (

54. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺨﺎﻣﺲ‬:‫اﻟ‬‫اﻟﻔﻴﺰﻳﺎﺋﻴﺔ‬ ‫ﺒﺼﺮﻳﺎت‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-55-
‫اﻟـﻀﻮء‬ ‫ﺗﺪاﺧﻞ‬:‫ﻀﻮﺋﯿﺔ‬‫اﻟ‬ ‫ﺎت‬‫اﻟﻤﻮﺟ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺮ‬‫اﻛﺜ‬ ‫او‬ ‫ﺴﻠﺘﯿﻦ‬‫ﺳﻠ‬ ‫ﺐ‬‫ﺗﺮاﻛ‬ ‫ﻦ‬‫ﻋ‬ ‫ﺌﺔ‬‫اﻟﻨﺎﺷ‬ ‫ﻀﻮﺋﯿﺔ‬‫اﻟ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ﻊ‬‫ﺗﻮزﯾ‬ ‫ﺎدة‬‫اﻋ‬ ‫ﺎھﺮة‬‫ظ‬ ‫ﻮ‬‫ھ‬
‫واﺣﺪ‬ ‫ان‬ ‫ﻓﻲ‬ ‫واﺣﺪة‬ ‫ﻧﻘﻄﺔ‬ ‫ﻧﺤﻮ‬ ‫وﺗﺘﺠﮭﺎن‬ ‫واﺣﺪ‬ ‫وﺳﻂ‬ ‫وﻓﻲ‬ ‫واﺣﺪ‬ ‫ﺑﻤﺴﺘﻮ‬ ‫اﻧﺘﺸﺎرھﻤﺎ‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﺘﺸﺎﻛﮭﺔ‬.
‫اﻟﺒﺼﺮي‬ ‫اﻟﻤﺴﺎر‬ ‫ﻃﻮل‬:‫ﻟﻼز‬ ‫ﺴﮫ‬‫ﻧﻔ‬ ‫ﺑﺎﻟﺰﻣﻦ‬ ‫اﻟﻔﺮاغ‬ ‫ﻓﻲ‬ ‫اﻟﻀﻮء‬ ‫ﯾﻘﻄﻌﮭﺎ‬ ‫اﻟﺘﻲ‬ ‫اﻹزاﺣﺔ‬ ‫ھﻮ‬‫ﺎدي‬‫اﻟﻤ‬ ‫ﻂ‬‫اﻟﻮﺳ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺎ‬‫ﯾﻘﻄﻌﮭ‬ ‫ﻲ‬‫اﻟﺘ‬ ‫ﺔ‬‫اﺣ‬
‫اﻟﺸﻔﺎف‬.
‫اﻟﺒﺼﺮي‬ ‫اﻟﻤﺴﺎر‬ ‫ﻓﺮق‬ ‫ﺣﺴﺎب‬:
‫ﺼﺪرﯾﻦ‬ ‫اﻟﻤ‬ ‫ﻦ‬ ‫ﻋ‬ ‫ﺪ‬ ‫واﺣ‬ ‫ﻮر‬ ‫ﺑﻄ‬ ‫ﺎن‬ ‫ﺗﻨﺒﻌﺜ‬ ‫ﻮﺋﯿﺘﯿﻦ‬ ‫ﺿ‬ ‫ﻮﺟﺘﯿﻦ‬ ‫ﻣ‬ ‫ﯿﻦ‬ ‫ﺑ‬ ‫ﺼﺮي‬ ‫اﻟﺒ‬ ‫ﺴﺎر‬ ‫اﻟﻤ‬ ‫ﻮل‬ ‫ط‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺮق‬ ‫اﻟﻔ‬ ‫ﺴﺎب‬ ‫ﻟﺤ‬)s2,s1(
‫اﻟﻨﻘﻄﺔ‬ ‫إﻟﻰ‬ ‫واﻟﻮاﺻﻠﺘﯿﻦ‬)P(‫اﻻﺗﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻧﺴﺘﺨﺪم‬:
‫ﺣﯿﺚ‬:
l∆:‫اﻟﻤﻮﺟﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﺼﺮي‬ ‫اﻟﻤﺴﺎر‬ ‫ﻓﺮق‬ ‫ﺗﻤﺜﻞ‬.
1l:‫ﺼﺪر‬ ‫اﻟﻤ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺔ‬ ‫اﻟﻤﻨﺒﻌﺜ‬ ‫ﺎت‬‫ﻟﻠﻤﻮﺟ‬ ‫ﺼﺮي‬ ‫اﻟﺒ‬ ‫ﺴﺎر‬‫اﻟﻤ‬ ‫ﻮل‬‫ط‬)S1(‫ﺔ‬‫اﻟﻨﻘﻄ‬ ‫ﻰ‬ ‫إﻟ‬ ‫ﻠﺔ‬‫واﻟﻮاﺻ‬)P.(‫ﺎ‬ ‫ﺗﻘﻄﻌﮭ‬ ‫ﻲ‬‫اﻟﺘ‬ ‫ﺴﺎﻓﺔ‬ ‫اﻟﻤ‬ ‫او‬
‫اﻟﻤﺼﺪر‬ ‫ﻣﻦ‬ ‫اﻟﻤﻮﺟﺎت‬)S1(‫اﻟﻨﻘﻄﺔ‬ ‫ﺑﺎﺗﺠﺎه‬)P. (
2l:‫ﻟﻠﻤ‬ ‫ﺼﺮي‬‫اﻟﺒ‬ ‫ﺴﺎر‬‫اﻟﻤ‬ ‫ﻮل‬‫ط‬‫ﺼﺪر‬‫اﻟﻤ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺔ‬‫اﻟﻤﻨﺒﻌﺜ‬ ‫ﺎت‬‫ﻮﺟ‬)S2(‫ﺔ‬‫اﻟﻨﻘﻄ‬ ‫ﻰ‬‫إﻟ‬ ‫ﻠﺔ‬‫واﻟﻮاﺻ‬)P.(‫ﺎ‬‫ﺗﻘﻄﻌﮭ‬ ‫ﻲ‬‫اﻟﺘ‬ ‫ﺴﺎﻓﺔ‬‫اﻟﻤ‬ ‫او‬
‫اﻟﻤﺼﺪر‬ ‫ﻣﻦ‬ ‫اﻟﻤﻮﺟﺎت‬)S2(‫اﻟﻨﻘﻄﺔ‬ ‫ﺑﺎﺗﺠﮫ‬)P. (
‫اﻟ‬ ‫ﻓﺮق‬ ‫ﺑﻴﻦ‬ ‫اﻟﻌﻼﻗﺔ‬‫ﻄﻮر‬‫اﻟ‬ ‫وﻓﺮق‬ ‫ﻣﻮﺟﺘﻴﻦ‬ ‫ﺑﻴﻦ‬‫اﻟﺒﺼﺮي‬ ‫ﻤﺴﺎر‬‫ﺑﻴﻨﻬﻤﺎ‬:
‫ﻮر‬ ‫اﻟﻄ‬ ‫ﺮق‬‫ﻓ‬ ‫ان‬)Ф(‫ﺔ‬ ‫اﻟﻨﻘﻄ‬ ‫ﻰ‬ ‫إﻟ‬ ‫ﻠﺘﯿﻦ‬ ‫اﻟﻮاﺻ‬ ‫ﻮﺟﺘﯿﻦ‬‫اﻟﻤ‬ ‫ﯿﻦ‬ ‫ﺑ‬P‫ﺑ‬ ‫ﺼﺮي‬ ‫اﻟﺒ‬ ‫ﺴﺎر‬ ‫اﻟﻤ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺪده‬‫ﯾﺤ‬‫ﻖ‬ ‫وﻓ‬ ‫ﻰ‬ ‫ﻋﻠ‬ ‫ﻮﺟﺘﯿﻦ‬ ‫اﻟﻤ‬ ‫ﯿﻦ‬
‫اﻻﺗﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬:
‫ﻋﻨـﺪ‬ ‫ﺑﻴﻨﻬﻤـﺎ‬ ‫اﻟﺤﺎﺻـﻞ‬ ‫اﻟﺘـﺪاﺧﻞ‬ ‫ﻧـﻮع‬ ‫ﻣﻌﺮﻓـﺔ‬ ‫ﺑﻌـﺪ‬ ‫اﻟـﻀﻮﺋﻴﺘﻴﻦ‬ ‫اﻟﻤـﻮﺟﺘﻴﻦ‬ ‫ﺑـﻴﻦ‬ ‫اﻟﺒـﺼﺮي‬ ‫اﻟﻤـﺴﺎر‬ ‫ﻓـﺮق‬ ‫ﺣـﺴﺎب‬ ‫ﻳﻤﻜﻦ‬ ‫ﻛﺬﻟﻚ‬
‫اﻟﻨﻘﻄﺔ‬)P(‫وﻛﺎﻻﺗﻲ‬:
1(‫واﻟﻤﻨﺒﻌﺜﺘﯿ‬ ‫اﻟﻤﺘﺸﺎﻛﮭﺘﯿﻦ‬ ‫اﻟﻀﻮﺋﯿﺘﯿﻦ‬ ‫اﻟﻤﻮﺟﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫ﺑﻨﺎء‬ ‫اﻟﺘﺪاﺧﻞ‬ ‫ﯾﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬‫اﻟﻤﺼﺪرﯾﻦ‬ ‫ﻣﻦ‬ ‫ﻦ‬)S2,S1(‫ﺴﺎر‬‫اﻟﻤ‬ ‫ﻓﺮق‬ ‫ﻓﺎن‬
‫اﻵﺗﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫ﯾﻌﻄﻰ‬ ‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﺒﺼﺮي‬:
‫ﺮق‬‫ﻓ‬ ‫ﻮن‬‫ﯾﻜ‬ ‫ﺪﻣﺎ‬‫ﻋﻨ‬ ‫ﺸﺎﻛﮭﺔ‬‫اﻟﻤﺘ‬ ‫ﻀﻮﺋﯿﺔ‬‫اﻟ‬ ‫ﺎت‬‫اﻟﻤﻮﺟ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺴﻠﺘﯿﻦ‬‫ﺳﻠ‬ ‫ﺎد‬‫اﺗﺤ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺼﻞ‬‫ﯾﺤ‬ ‫ﺔ‬‫ﻧﻘﻄ‬ ‫ﻓﻲ‬ ‫اﻟﺒﻨﺎء‬ ‫اﻟﺘﺪاﺧﻞ‬ ‫ان‬ ‫ﯾﻌﻨﻲ‬ ‫وھﺬا‬
‫ﺻﺤﯿ‬ ‫اﻋﺪاد‬ ‫او‬ ‫ﺻﻔﺮ‬ ‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﺒﺼﺮي‬ ‫اﻟﻤﺴﺎر‬‫ان‬ ‫أي‬ ‫اﻟﻤﻮﺟﺔ‬ ‫طﻮل‬ ‫ﻣﻦ‬ ‫ﺤﺔ‬:
......3,2,1,0 λλλ=∆l
‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫ﻓﯿﻜﻮن‬)Ф(‫ﻣﻦ‬ ‫زوﺟﯿﺔ‬ ‫اﻋﺪاد‬ ‫او‬ ‫ﺻﻔﺮ‬ ‫ﯾﺴﺎوي‬ ‫ﺑﯿﻨﮭﻤﺎ‬)π rad(‫ان‬ ‫أي‬:
Ф =0 , 2π , 4π , 6π , ……… rad
2(‫ﺼﺪرﯾﻦ‬‫اﻟﻤ‬ ‫ﻦ‬‫ﻣ‬ ‫ﯿﻦ‬‫واﻟﻤﻨﺒﻌﺜﺘ‬ ‫ﺸﺎﻛﮭﺘﯿﻦ‬‫اﻟﻤﺘ‬ ‫ﻀﻮﺋﯿﺘﯿﻦ‬‫اﻟ‬ ‫ﻮﺟﺘﯿﻦ‬‫اﻟﻤ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﻼف‬‫اﺗ‬ ‫ﺪاﺧﻞ‬‫اﻟﺘ‬ ‫ﻮن‬‫ﯾﻜ‬ ‫ﻋﻨﺪﻣﺎ‬)S2,S1(‫ﺮق‬‫ﻓ‬ ‫ﺎن‬‫ﻓ‬
‫اﻟﻤﺴ‬‫اﻻﺗﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫ﯾﻌﻄﻰ‬ ‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﺒﺼﺮي‬ ‫ﺎر‬:
.........3,2,1,0m)
2
1
m( =λ+=∆l
.........3,2,1,0mm =λ=∆l
12 lll −=∆
l∆
λ
π
=Φ
2
)‫اﻟﺒﻨﺎء‬ ‫اﻟﺘﺪاﺧﻞ‬ ‫ﺷﺮط‬(
)‫اﻻ‬ ‫اﻟﺘﺪاﺧﻞ‬ ‫ﺷﺮط‬‫ﺗﻼف‬(

55. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺨﺎﻣﺲ‬:‫اﻟ‬‫اﻟﻔﻴﺰﻳﺎﺋﻴﺔ‬ ‫ﺒﺼﺮﻳﺎت‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-56-
,........3,2,1,0m ±±±=
‫ﺪﻣﺎ‬‫ﻋﻨ‬ ‫ﺴﯿﻦ‬‫ﻣﺘﻌﺎﻛ‬ ‫ﻮرﯾﻦ‬‫ﺑﻄ‬ ‫ﺸﺎﻛﮭﺔ‬‫اﻟﻤﺘ‬ ‫ﺎت‬‫اﻟﻤﻮﺟ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺴﻠﺘﯿﻦ‬‫ﺳﻠ‬ ‫اﺗﺤﺎد‬ ‫ﻣﻦ‬ ‫ﯾﺤﺼﻞ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻓﻲ‬ ‫اﻻﺗﻼف‬ ‫اﻟﺘﺪاﺧﻞ‬ ‫ان‬ ‫ﯾﻌﻨﻲ‬ ‫وھﺬا‬
‫ا‬ ‫أي‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬ ‫ﻧﺼﻒ‬ ‫ﻣﻦ‬ ‫ﻓﺮدﯾﺔ‬ ‫اﻋﺪاد‬ ‫ﯾﺴﺎوي‬ ‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﺒﺼﺮي‬ ‫اﻟﻤﺴﺎر‬ ‫ﻓﺮق‬ ‫ﯾﻜﻮن‬‫ن‬:
.......
2
5
,
2
3
,
2
1
λλλ=∆l
‫ﻣﻦ‬ ‫ﻓﺮدﯾﺔ‬ ‫اﻋﺪاد‬ ‫ﯾﺴﺎوي‬ ‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﻄﻮر‬ ‫ﻓﺮق‬ ‫ﻓﯿﻜﻮن‬)π rad. (‫ان‬ ‫أي‬:
Ф = π , 3π , 5π , …….
‫ﺗﻨﻮﻳﻪ‬/
‫ﻓﻲ‬‫ﻳﻮﻧﻚ‬ ‫ﺷﻘﻲ‬ ‫ﺗﺠﺮﺑﺔ‬‫ﻓﺎن‬:
v‫اﻟﻤﺮﻛﺰي‬ ‫اﻟﻬﺪب‬:‫اﻟﺸﻘﻴﻦ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻣﻨﺘﺼﻒ‬ ‫إﻟﻰ‬ ‫اﻟﻤﻘﺎﺑﻞ‬ ‫اﻻوﺳﻂ‬ ‫اﻟﻤﻀﻲء‬ ‫اﻟﻬﺪب‬ ‫ﻫﻮ‬.
v‫ا‬ ‫ﻫﺪب‬‫ﻟﺘﺪاﺧﻞ‬:‫اﻟﺸﺎﺷﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺗﻈﻬﺮ‬ ‫اﻟﺘﻌﺎﻗﺐ‬ ‫وﻋﻠﻰ‬ ‫ﻣﻌﺘﻤﺔ‬ ‫ﻣﻨﺎﻃﻖ‬ ‫ﺗﺘﺨﻠﻠﻬﺎ‬ ‫ﻣﻀﻴﺌﺔ‬ ‫ﻣﻨﺎﻃﻖ‬ ‫ﻫﻲ‬.
v‫اﻳﺠﺎد‬ ‫ﻳﻤﻜﻦ‬‫ﺑﻌﺪ‬)‫ﻣﻮﻗﻊ‬ ‫او‬(‫اﻟﺮﺗﺒﺔ‬ ‫ذو‬ ‫اﻟﻤﻈﻠﻢ‬ ‫او‬ ‫اﻟﻤﻀﻲء‬ ‫اﻟﻬﺪب‬m‫اﻵﺗﻴﺔ‬ ‫ﻟﻠﻌﻼﻗﺎت‬ ‫وﻓﻘﺎ‬ ‫اﻟﻤﺮﻛﺰي‬ ‫اﻟﻬﺪب‬ ‫ﻋﻦ‬:
‫ﺣﯿﺚ‬:
ym:‫ﻣﻮ‬ ‫او‬ ‫ﺑﻌﺪ‬‫رﺗﺒﺘﮫ‬ ‫اﻟﺬي‬ ‫اﻟﻤﻈﻠﻢ‬ ‫او‬ ‫اﻟﻤﻀﻲء‬ ‫اﻟﮭﺪب‬ ‫ﻗﻊ‬)m(‫اﻟﻤﻀﻲء‬ ‫اﻟﻤﺮﻛﺰي‬ ‫اﻟﮭﺪب‬ ‫ﻋﻦ‬.
λ:‫اﻟﻤﺴﺘﻌﻤﻞ‬ ‫اﻟﻠﻮن‬ ‫اﻻﺣﺎدي‬ ‫اﻟﻀﻮء‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬.
L:‫اﻟﺸﻘﯿﻦ‬ ‫ﺣﺎﺟﺰ‬ ‫ﻋﻦ‬ ‫اﻟﺸﺎﺷﺔ‬ ‫ﺑﻌﺪ‬.
d:‫اﻟﺸﻘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬.
m:‫اﻟﻤﻈﻠﻢ‬ ‫او‬ ‫اﻟﻤﻀﻲء‬ ‫اﻟﮭﺪب‬ ‫رﺗﺒﺔ‬.
‫اﻣﺎ‬‫ﻟﺤﺴﺎب‬‫اﻟﻤﻈﻠـﻢ‬ ‫او‬ ‫اﻟﻤـﻀﻲء‬ ‫اﻟﻬـﺪب‬ ‫اﻧﺤـﺮاف‬ ‫زاوﻳـﺔ‬ ‫او‬ ‫ﺣﻴـﻮد‬ ‫زاوﻳـﺔ‬‫ﻋـﻦ‬‫اﺳـﺘﺨﺪام‬ ‫ﻳﻤﻜـﻦ‬ ‫اﻟﻤـﻀﻲء‬ ‫اﻟﻤﺮﻛـﺰي‬ ‫اﻟﻬـﺪب‬
‫اﻵﺗﻴﺔ‬ ‫اﻟﻌﻼﻗﺔ‬:
‫ﺣﯿﺚ‬:
θ:‫اﻻﻧﺤﺮاف‬ ‫زاوﯾﺔ‬ ‫او‬ ‫اﻟﺤﯿﻮد‬ ‫زاوﯾﺔ‬.
y:‫اﻟﻤﻀﻲ‬ ‫اﻟﻤﺮﻛﺰي‬ ‫اﻟﮭﺪب‬ ‫ﻣﺮﻛﺰ‬ ‫ﻋﻦ‬ ‫اﻟﻤﻈﻠﻢ‬ ‫او‬ ‫اﻟﻤﻀﻲء‬ ‫اﻟﮭﺪب‬ ‫ﻣﺮﻛﺰ‬ ‫ﺑﻌﺪ‬.
L:‫اﻟﺸﻘﯿﻦ‬ ‫ﺣﺎﺟﺰ‬ ‫ﻋﻦ‬ ‫اﻟﺸﺎﺷﺔ‬ ‫ﺑﻌﺪ‬.
‫ﻛﻞ‬:
π=λπ=λ
2
1
,2
d
L)
2
1
m(
ym
λ+
=
d
Lm
ym
λ
= )‫اﻟﻤﻀﻴ‬ ‫ُﺪب‬‫ﻬ‬‫ﻟﻠ‬‫ﺌﺔ‬(
)‫اﻟﻤﻈﻠﻤﺔ‬ ‫ُﺪب‬‫ﻬ‬‫ﻟﻠ‬(
L
y
tan =θ

56. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺨﺎﻣﺲ‬:‫اﻟ‬‫اﻟﻔﻴﺰﻳﺎﺋﻴﺔ‬ ‫ﺒﺼﺮﻳﺎت‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-57-
‫اﻧﺘﺒﻪ‬/
‫اﻟﻤﻀﻲء‬ ‫اﻟﮭﺪب‬ ‫رﺗﺒﺔ‬)m(‫ﺗﻄﺎﺑﻖ‬‫ﺮﻗﻢ‬‫اﻟ‬ ‫ﻦ‬‫ﻋ‬ ‫ﺪ‬‫واﺣ‬ ‫ﺪار‬‫ﺑﻤﻘ‬ ‫ﻨﻘﺺ‬‫ﺗ‬ ‫ﺘﻢ‬‫اﻟﻤﻌ‬ ‫ﺪب‬‫اﻟﮭ‬ ‫ﺔ‬‫رﺗﺒ‬ ‫ﺎ‬‫ﺑﯿﻨﻤ‬ ، ‫ﺴﺆال‬‫اﻟ‬ ‫ﻲ‬‫ﻓ‬ ‫ﻰ‬‫اﻟﻤﻌﻄ‬ ‫اﻟﺮﻗﻢ‬
‫اﻟﺴﺆال‬ ‫ﻓﻲ‬ ‫اﻟﻤﻌﻄﻰ‬.
‫ﻣﺜﻼ‬:(m=0)، ‫اﻟﻤﻀﻲء‬ ‫اﻟﻤﺮﻛﺰي‬ ‫ﻟﻠﮭﺪب‬)(m=1، ‫اﻻول‬ ‫ﻟﻠﻤﻀﻲء‬m=2)(‫وھﻜﺬا‬ ‫اﻟﺜﺎﻧﻲ‬ ‫اﻟﻤﻀﻲء‬ ‫ﻟﻠﮭﺪب‬
‫ﺑﯿﻨﻤﺎ‬)m=0(، ‫اﻻول‬ ‫اﻟﻤﻌﺘﻢ‬ ‫ﻟﻠﮭﺪب‬)(m=1‫وھﻜﺬا‬ ‫اﻟﺜﺎﻧﻲ‬ ‫اﻟﻤﻌﺘﻢ‬ ‫ﻟﻠﮭﺪب‬.
‫اﻟ‬ ‫اﻣﺎ‬‫اﻟﻤﺘﺠـﺎورة‬ ‫اﻟﻬـﺪب‬ ‫ﺑﻴﻦ‬ ‫ﻔﻮاﺻﻞ‬)‫اﻟﻤﻈﻠﻤـﺔ‬ ‫او‬ ‫اﻟﻤـﻀﻴﺌﺔ‬(‫ﻟﻬـﺎ‬ ‫وﻳﺮﻣـﺰ‬ ‫اﻟﻬـﺪب‬ ‫ﻓﺎﺻـﻠﺔ‬ ‫ﻓﺘـﺴﻤﻰ‬)∆y(‫وﺗﻌﻄـﻰ‬‫وﻓﻘـﺎ‬
‫اﻻﺗﻴﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬:
‫ﺣﯿﺚ‬)∆y(‫ﻣﺘﺘﺎﻟﯿﯿﻦ‬ ‫ھﺪﺑﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫او‬ ‫اﻟﺘﺪاﺧﻞ‬ ‫ھﺪب‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﻌﺪ‬ ‫او‬ ‫اﻟﮭﺪب‬ ‫ﻓﺎﺻﻠﺔ‬)‫ﻣﻌﺘﻤﯿﻦ‬ ‫او‬ ‫ﻣﻀﯿﺌﯿﻦ‬.(
‫س‬/‫ﻋﻼ‬ ‫اﺷﺘﻖ‬ ‫ﯾﻮﻧﻚ‬ ‫ﺗﺠﺮﺑﺔ‬ ‫ﻓﻲ‬‫اﻟﺘﺪاﺧﻞ‬ ‫ھﺪب‬ ‫ﺑﯿﻦ‬ ‫اﻟﻔﺎﺻﻠﺔ‬ ‫ﻟﺤﺴﺎب‬ ‫ﻗﺔ‬.
‫ج‬/
d
L
)
2
1
m
2
3
m(
d
L
y
)]
2
1
m()
2
3
m[(
d
L
d
L)
2
1
m(
d
L)
2
3
m(
yyy
or
d
L
)m1m(
d
L
d
Lm
d
L)1m(
yyy
2
1
m
2
3
m
m1m
λ
=−−+
λ
=∆
+−+
λ
=
λ+
−
λ+
=−=∆
λ
=−+
λ
=
λ
−
λ+
=−=∆
++
+
‫س‬/‫اﻟﻤﺮﻛﺰ‬ ‫ﻋﻦ‬ ‫اﻟﺸﺎﺷﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﻀﯿﺌﺔ‬ ‫اﻟﮭﺪب‬ ‫ﻣﻮاﻗﻊ‬ ‫ﻟﺤﺴﺎب‬ ‫ﻋﻼﻗﺔ‬ ‫اﺷﺘﻖ‬ ‫ﯾﻮﻧﻚ‬ ‫ﺗﺠﺮﺑﺔ‬ ‫ﻓﻲ‬.
‫ج‬/
d
Lm
y
L
y
.dm
)
L
y
(tan
L
y
sintansin
sindmsind
m
λ
=⇒=λ∴
=θ=θ⇒θ=θ
θ=λ⇒θ=∆
λ=∆
Q
l
l
‫س‬/‫اﻟﻤﺮﻛﺰ‬ ‫ﻋﻦ‬ ‫اﻟﺸﺎﺷﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﻌﺘﻤﺔ‬ ‫اﻟﮭﺪب‬ ‫ﻣﻮاﻗﻊ‬ ‫ﻟﺤﺴﺎب‬ ‫ﻋﻼﻗﺔ‬ ‫اﺷﺘﻖ‬ ‫ﯾﻮﻧﻚ‬ ‫ﺗﺠﺮﺑﺔ‬ ‫ﻓﻲ‬.
‫ج‬/
d
L)
2
1
m(
y
L
y
.d)
2
1
m(
)
L
y
(tan
L
y
sintansin
sind)
2
1
m(sind
)
2
1
m(
λ+
=⇒=λ+∴
=θ=θ⇒θ=θ
θ=λ+⇒θ=∆
λ+=∆
Q
l
l
d
L
y
λ
=∆

57. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺨﺎﻣﺲ‬:‫اﻟ‬‫اﻟﻔﻴﺰﻳﺎﺋﻴﺔ‬ ‫ﺒﺼﺮﻳﺎت‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-58-
‫اﻟﺤﻴﻮد‬ ‫ﻣﺤﺰز‬:‫ھﻮ‬‫أداة‬‫ﻓﻲ‬ ‫ﻣﻔﯿﺪة‬‫و‬ ‫اﻻطﯿﺎف‬ ‫دراﺳﺔ‬‫ﺔ‬‫اﻟﻤﺘﻮازﯾ‬ ‫اﻟﺤﺰوز‬ ‫ﻣﻦ‬ ‫ﻛﺒﯿﺮ‬ ‫ﻋﺪد‬ ‫ﻣﻦ‬ ‫ﯾﺘﺎﻟﻒ‬ ‫اذ‬ ‫اﻟﻀﻮء‬ ‫ﻣﺼﺎدر‬ ‫ﺗﺤﻠﯿﻞ‬
‫اﻟﻤﺘﻘﺎرﺑﺔ‬‫اﻟﻤﺘﺴﺎوﯾﺔ‬ ‫اﻟﻔﻮاﺻﻞ‬ ‫ذات‬.
‫اﻟﻤﺤﺰز‬ ‫ﺛﺎﺑﺖ‬)d(:‫ﺑ‬ ‫اﻟﻤﺴﺎﻓﺔ‬‫ﺟﺪا‬ ‫ﺻﻐﯿﺮ‬ ‫وﻣﻘﺪاره‬ ‫اﻟﻤﺤﺰز‬ ‫ﻓﻲ‬ ‫ﻣﺘﺘﺎﻟﯿﯿﻦ‬ ‫ﺣﺰﯾﻦ‬ ‫ﻛﻞ‬ ‫ﯿﻦ‬.
‫ﻟ‬ ‫وﻓﻘﺎ‬ ‫اﻟﻤﺤﺰز‬ ‫ﺛﺎﺑﺖ‬ ‫ﻳﺤﺴﺐ‬‫ﻤﺎ‬‫ﻳﺄﺗﻲ‬:
‫ﺣﯿﺚ‬:
W:‫اﻟﻤﺤﺰز‬ ‫ﻋﺮض‬‫ﺣﯿﺚ‬)w=1cm(.
N:‫اﻟﺤﺰوز‬ ‫ﻋﺪد‬‫ﺑﯿﻦ‬ ‫اﻟﻤﺤﺰز‬ ‫ﻣﻦ‬ ‫اﻟﻮاﺣﺪ‬ ‫اﻟﺴﻨﺘﻤﺘﺮ‬ ‫ﻓﻲ‬ ‫اﻟﺤﺰوز‬ ‫ﻋﺪد‬ ‫ﯾﺘﺮاوح‬ ‫ﺣﯿﺚ‬(1000-10000)line/cm.
‫اﻟﺤﺰوز‬ ‫ﻋﺪد‬ ‫ﻛﺎن‬ ‫ﻓﻠﻮ‬5000line/cm‫اﻟﻤﺤﺰز‬ ‫ﺛﺎﺑﺖ‬ ‫ﻓﺎن‬ ‫ﻣﺜﻼ‬)d(‫ﯾﻜﻮن‬:
cm102
cm/line5000
1
N
w
d 4−
×===
v‫ﻓ‬‫ﻳﻜﻮن‬ ‫ﻌﻨﺪﻣﺎ‬‫اﻟﺒﺼﺮي‬ ‫اﻟﻤﺴﺎر‬ ‫ﻓﺮق‬‫ﻣﺘﺠـﺎورﻳﻦ‬ ‫ﺷـﻘﻴﻦ‬ ‫أي‬ ‫ﻣـﻦ‬ ‫ﺻـﺎدرﻳﻦ‬ ‫ﺷﻌﺎﻋﻴﻦ‬ ‫ﺑﻴﻦ‬)‫ﻣﺘﺘـﺎﻟﻴﻴﻦ‬(‫ﻳـﺴﺎوي‬ ‫اﻟﻤﺤـﺰز‬ ‫ﻓـﻲ‬
‫ـﺪة‬‫ـ‬‫واﺣ‬ ‫ـﺔ‬‫ـ‬‫ﻣﻮﺟ‬ ‫ـﻮل‬‫ـ‬‫ﻃ‬)λ(‫ـﺔ‬‫ـ‬‫اﻟﻤﻮﺟ‬ ‫ـﻮل‬‫ـ‬‫ﻃ‬ ‫ـﻦ‬‫ـ‬‫ﻣ‬ ‫ـﺤﻴﺤﺔ‬‫ـ‬‫ﺻ‬ ‫ـﺪاد‬‫ـ‬‫اﻋ‬ ‫او‬)λm(‫ـﺪاﺧﻞ‬‫ـ‬‫اﻟﺘ‬ ‫ـﺎن‬‫ـ‬‫ﻓ‬‫ـﻮن‬‫ـ‬‫ﻳﻜ‬ ‫ـﺎت‬‫ـ‬‫اﻟﻤﻮﺟ‬ ‫ـﻴﻦ‬‫ـ‬‫ﺑ‬‫ـﺎء‬‫ـ‬‫ﺑﻨ‬
‫ﻣﻀﻴﺌﺔ‬ ‫اﻟﻬﺪب‬ ‫وﺗﻈﻬﺮ‬‫اﻟﺸﺎﺷﺔ‬ ‫ﻋﻠﻰ‬‫ووﻓ‬‫ﻟﻠﻌﻼﻗﺔ‬ ‫ﻘﺎ‬‫اﻵﺗﻴﺔ‬:
,
‫اﻟﻤﻄﻴﺎف‬ ‫ﺟﻬﺎز‬ ‫ﺑﺎﺳﺘﻌﻤﺎل‬ ‫اﻟﻠﻮن‬ ‫اﺣﺎدي‬ ‫ﻟﻀﻮء‬ ‫اﻟﻤﻮﺟﻲ‬ ‫اﻟﻄﻮل‬ ‫ﻟﻘﻴﺎس‬ ‫ﺗﺴﺘﺨﺪم‬ ‫ان‬ ‫ﻳﻤﻜﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫وﻫﺬه‬.
‫ﺣﯿﺚ‬:
d:‫اﻟﻤﺤﺰز‬ ‫ﺛﺎﺑﺖ‬)
N
W
d =(‫ﺑﻮﺣﺪة‬)cm.(
θ:‫اﻟﮭﺪ‬ ‫ﺣﯿﻮد‬ ‫زاوﯾﺔ‬‫رﺗﺒﺘﮫ‬ ‫اﻟﺬي‬ ‫ب‬m‫اﻟﻤﺮﻛﺰي‬ ‫اﻟﮭﺪب‬ ‫ﻋﻦ‬.
θsind:‫اﻟﻤﺤﺰز‬ ‫ﻓﻲ‬ ‫ﻣﺘﺠﺎورﯾﻦ‬ ‫ﺷﻘﯿﻦ‬ ‫ﻋﻦ‬ ‫ﺻﺎدرﯾﻦ‬ ‫ﺷﻌﺎﻋﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﺼﺮي‬ ‫اﻟﻤﺴﺎر‬ ‫ﻓﺮق‬.
λ:‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﺤﺰز‬ ‫ﻓﻲ‬ ‫اﻟﻤﺴﺘﻌﻤﻞ‬ ‫اﻟﻀﻮء‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬)cm. (
m:‫اﻟﻤﻀﻲء‬ ‫اﻟﮭﺪب‬ ‫رﺗﺒﺔ‬.
‫اﻧﺘﺒﻪ‬:
)m(‫اﻟﻄ‬ ‫ﻓﻲ‬ ‫ﻣﻀﯿﺌﺔ‬ ‫ﻣﺮﺗﺒﺔ‬ ‫ﻻﺧﺮ‬‫اﻻﺗﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫ﻋﻨﮭﺎ‬ ‫ﯾﻌﺒﺮ‬ ‫اﻟﻨﺎﺗﺞ‬ ‫ﯿﻒ‬:
‫ھﻲ‬ ‫ﻣﻀﯿﺌﺔ‬ ‫ﻣﺮﺗﺒﺔ‬ ‫ﻻﺧﺮ‬ ‫اﻟﻀﻮء‬ ‫ﺣﯿﻮد‬ ‫زاوﯾﺔ‬ ‫ﺣﯿﺚ‬)90º(‫ان‬ ‫أي‬)°=θ 90(‫وان‬)sin90º=1. (
v‫اﻟﺼﻮر‬ ‫ﻋﺪد‬ ‫ﻟﻤﻌﺮﻓﺔ‬ ‫اﻣﺎ‬)n(‫ﯾﺠﺐ‬ ‫اﻟﺸﺎﺷﺔ‬ ‫ﻋﻠﻰ‬ ‫واﻟﻤﺘﻜﻮﻧﺔ‬ ‫اﻟﻤﻀﯿﺌﺔ‬‫ﻀﯿﺌﺔ‬‫ﻣ‬ ‫ﺔ‬‫ﻣﺮﺗﺒ‬ ‫اﺧﺮ‬ ‫ﻣﻌﺮﻓﺔ‬)‫ﺔ‬‫زاوﯾ‬ ‫ﺪ‬‫ﻋﻨ‬90º(‫ﻢ‬‫ﺛ‬
‫اﻟﺘﺎﻟﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻧﺴﺘﺨﺪم‬:
‫ﺣﯿﺚ‬:m:‫ﻋﻨﺪ‬ ‫ﻣﻀﯿﺌﺔ‬ ‫ﻣﺮﺗﺒﺔ‬ ‫آﺧﺮ‬)θ=90º. (
1m2n +=
‫ﻣﻀﻴﺌﺔ‬ ‫ﻣﺮﺗﺒﺔ‬ ‫اﺧﺮ‬ ‫ﻻﻳﺠﺎد‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻫﺬه‬ ‫ﺗﺴﺘﺨﺪم‬
......,3,2,1m +++=λ=θ msind
N
w
d =
λ
θ
=
sind
m

58. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺨﺎﻣﺲ‬:‫اﻟ‬‫اﻟﻔﻴﺰﻳﺎﺋﻴﺔ‬ ‫ﺒﺼﺮﻳﺎت‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-59-
‫ﻣﻼﺣﻈﺎت‬/
1-‫رﺗﺒﺘﮭﺎ‬ ‫ﻣﻀﯿﺌﺔ‬ ‫ﺻﻮرة‬ ‫رؤﯾﺔ‬ ‫ﯾﻤﻜﻦ‬ ‫ھﻞ‬ ‫ﻟﻤﻌﺮﻓﺔ‬m‫ﻣﻨﺎ‬ ‫ﯾﺘﻄﻠﺐ‬ ‫اﻟﺸﺎﺷﺔ‬ ‫ﻋﻠﻰ‬‫اﯾﺠﺎد‬sinθ‫ﻛﺎن‬ ‫اذا‬ ‫ذﻟﻚ‬ ‫وﺑﻌﺪ‬:
a-sinθ > 1‫ﻻ‬‫واﺣﺪ‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫اﻟﺰاوﯾﺔ‬ ‫ﺟﯿﺐ‬ ‫ﯾﻜﻮن‬ ‫ان‬ ‫ﻻﺳﺘﺤﺎﻟﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﺗﻠﻚ‬ ‫رؤﯾﺔ‬ ‫ﯾﻤﻜﻦ‬.
b-1sin ≤θ‫اﻟﺼﻮرة‬ ‫ﺗﻠﻚ‬ ‫رؤﯾﺔ‬ ‫ﯾﻤﻜﻦ‬ ‫ﻧﻌﻢ‬ ‫ذﻟﻚ‬ ‫ﻋﻨﺪ‬.
2-‫ان‬‫ﺸﻘﻮق‬ ‫اﻟ‬ ‫ﻞ‬‫ﻋﻤ‬ ‫ﻞ‬‫ﺗﻌﻤ‬ ‫ﻲ‬‫ﻓﮭ‬ ‫ﺎ‬ ‫ﺧﻼﻟﮭ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﻀﻮء‬‫اﻟ‬ ‫ﺎذ‬ ‫ﺑﻨﻔ‬ ‫ﺴﻤﺢ‬ ‫ﺗ‬ ‫ﺰوز‬‫اﻟﺤ‬ ‫ﯿﻦ‬ ‫ﺑ‬ ‫ﻞ‬‫اﻟﻔﻮاﺻ‬ ‫ﺎ‬‫ﺑﯿﻨﻤ‬ ‫ﻀﻮء‬ ‫اﻟ‬ ‫ﺐ‬‫ﺗﺤﺠ‬ ‫ﺰوز‬‫اﻟﺤ‬
‫ﺟﺪا‬ ‫اﻟﻀﯿﻘﺔ‬.
3-line‫ﺧﻂ‬ ‫او‬ ‫ﺣﺰ‬ ‫ﺗﻌﻨﻲ‬.
‫ﺗﺬﻛﺮ‬:
‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اﻟﻜﮭﺮوﻣﻐﻨﺎطﯿﺴﯿﺔ‬ ‫ﻟﻠﻤﻮﺟﺎت‬ ‫اﻟﻌﺎﻣﺔ‬ ‫اﻟﻤﻌﺎدﻟﺔ‬ ‫ﺑﺎﺳﺘﻌﻤﺎل‬ ‫اﻟﻤﻮﺟﻲ‬ ‫واﻟﻄﻮل‬ ‫اﻟﺘﺮدد‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫اﯾﺠﺎد‬ ‫ﯾﻤﻜﻦ‬:
‫ﺑﺎﻟﻨﺎﻧﻮﻣﺘﺮ‬ ‫ﻋﺎدة‬ ‫ﯾﻘﺎس‬ ‫ﻓﮭﻮ‬ ‫اﻟﻀﻮء‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬ ‫ﻟﻘﺼﺮ‬ ‫وﺑﺎﻟﻨﻈﺮ‬)nm(‫ﻣﻦ‬ ‫وﻟﻠﺘﺤﻮﯾﻞ‬:
a-)nm(‫إﻟﻰ‬)m(‫ﻓﻲ‬ ‫اﻟﻤﻘﺪار‬ ‫ﻧﻀﺮب‬10-9
‫وﺑﺎﻟﻌﻜ‬‫ﻣﻦ‬ ‫اﻟﺘﺤﻮﯾﻞ‬ ‫ﻋﻨﺪ‬ ‫ﺲ‬)m(‫إﻟﻰ‬)nm(‫ﻓﻲ‬ ‫اﻟﻤﻘﺪار‬ ‫ﻧﻀﺮب‬109
.
b-)nm(‫إﻟﻰ‬)cm(‫ﻓﻲ‬ ‫اﻟﻤﻘﺪار‬ ‫ﻧﻀﺮب‬10-7
‫ﻣﻦ‬ ‫اﻟﺘﺤﻮﯾﻞ‬ ‫ﻋﻨﺪ‬ ‫وﺑﺎﻟﻌﻜﺲ‬)cm(‫إﻟﻰ‬)nm(‫ﻓﻲ‬ ‫ﻧﻀﺮب‬107
.
‫ﺑﺎﻻﻧﻌﻜﺎس‬ ‫اﻟﻀﻮء‬ ‫اﺳﺘﻘﻄﺎب‬:
‫ﺑﺤﯿ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺎء‬‫ﻣ‬ ‫ﻄﺢ‬ ‫ﺳ‬ ‫او‬ ‫ﺴﺘﻮﯾﺔ‬‫اﻟﻤ‬ ‫ﺎ‬‫اﻟﻤﺮاﯾ‬ ‫ﻞ‬‫ﻣﺜ‬ ‫ﺴﺔ‬‫ﻋﺎﻛ‬ ‫ﻄﻮح‬‫ﺳ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﻀﻮء‬ ‫اﻟ‬ ‫ﻘﻮط‬‫ﺳ‬ ‫ﺪ‬‫ﻋﻨ‬ ‫ﮫ‬ ‫اﻧ‬ ‫ﺎﻟﻮس‬‫ﻣ‬ ‫ﺎﻟﻢ‬‫اﻟﻌ‬ ‫ﺸﻒ‬‫اﻛﺘ‬‫او‬ ‫ﺮة‬
‫ﻣﺎﺋﻠﺔ‬ ‫وﺑﺼﻮرة‬ ‫اﻟﺰﺟﺎج‬‫وﺑﺄي‬‫ﻓﺎن‬ ‫ﺳﻘﻮط‬ ‫زاوﯾﺔ‬:
v‫ﻣﺴﺘﻮي‬ ‫وﻓﻲ‬ ‫ﺟﺰﺋﯿﺎ‬ ‫ﻣﺴﺘﻘﻄﺒﺎ‬ ‫ﯾﻜﻮن‬ ‫اﻟﻤﻨﻌﻜﺲ‬ ‫اﻟﻀﻮء‬‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻟﻤﺴﺘﻮي‬ ‫ﻣﻮاز‬
v‫اﻻﺷﻌﺔ‬ ‫ﺳﻘﻮط‬ ‫ﻣﺴﺘﻮي‬ ‫ﻓﻲ‬ ‫ﯾﻜﻮن‬ ‫اﻟﺜﺎﻧﻲ‬ ‫اﻟﻮﺳﻂ‬ ‫ﻓﻲ‬ ‫اﻟﻤﻨﻜﺴﺮ‬ ‫اﻟﻀﻮء‬.
‫ز‬ ‫او‬ ‫ﺑﺮوﺳـﺘﺮ‬ ‫زاوﻳـﺔ‬ ‫ﺗـﺴﻤﻰ‬ ‫ﻣﻌﻴﻨـﺔ‬ ‫زاوﻳـﺔ‬ ‫ﻋﻨـﺪ‬ ‫ﻛﻠﻴـﺎ‬ ‫اﺳـﺘﻮاﺋﻴﺎ‬ ‫ﻣـﺴﺘﻘﻄﺒﺎ‬ ‫ﻳـﺼﺒﺢ‬ ‫اﻟﻤـﻨﻌﻜﺲ‬ ‫اﻟﻀﻮء‬ ‫ان‬‫اﻻﺳـﺘﻘﻄﺎب‬ ‫اوﻳـﺔ‬
‫ورﻣﺰﻫﺎ‬)θp(‫اﻻﺳﺘﻘﻄﺎب‬ ‫زاوﻳﺔ‬ ‫ﺑﻴﻦ‬ ‫ﻋﻼﻗﺔ‬ ‫ﺑﺮوﺳﺘﺮ‬ ‫وﺟﺪ‬ ‫ﺣﻴﺚ‬)θp(‫اﻟﻮﺳﻂ‬ ‫اﻧﻜﺴﺎر‬ ‫وﻣﻌﺎﻣﻞ‬)n(‫ﻳﻠﻲ‬ ‫وﻛﻤﺎ‬:
‫ﺣﯿﺚ‬‫اﻟﻮﺳﻂ‬ ‫اﻧﻜﺴﺎر‬ ‫ﻣﻌﺎﻣﻞ‬)n(‫اﻟﻮﺣﺪات‬ ‫ﻣﻦ‬ ‫ﻣﺠﺮد‬ ‫ﻋﺪد‬ ‫وھﻮ‬‫و‬‫اﻻﺗﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﺑﺎﺣﺪى‬ ‫ﻋﻨﮫ‬ ‫ﯾﻌﺒﺮ‬:
or
cθ:‫اﻟﺤﺮﺟﺔ‬ ‫اﻟﺰاوﯾﺔ‬.
‫ﻣﻼﺣﻈﺎت‬/
1-‫ﺪث‬‫ﯾﺤ‬ ‫ﻻ‬ ‫ﺬﻟﻚ‬‫ﻟ‬ ‫ﻔﺮ‬‫ﺻ‬ ‫ﺴﺎوي‬‫ﺗ‬ ‫ﺴﻘﻮط‬‫اﻟ‬ ‫ﺔ‬‫زاوﯾ‬ ‫ﺎن‬‫ﻓ‬ ‫ﮫ‬‫ﻋﻠﯿ‬ ‫ﺔ‬‫ﻋﻤﻮدﯾ‬ ‫ﺼﻮرة‬‫وﺑ‬ ‫ﺎﻛﺲ‬‫ﻋ‬ ‫ﻄﺢ‬‫ﺳ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﻀﻮء‬‫اﻟ‬ ‫ﺴﻘﻂ‬‫ﯾ‬ ‫ﺪﻣﺎ‬‫ﻋﻨ‬
‫اﺳﺘﻘﻄﺎب‬.
2-‫ﯾﺴ‬ ‫ﻋﻨﺪﻣﺎ‬‫ﺘﻘﻄﺎب‬‫اﻻﺳ‬ ‫ﺔ‬‫زاوﯾ‬ ‫ﺴﺎوي‬‫ﺗ‬ ‫ﻻ‬ ‫ﻀﻮء‬‫اﻟ‬ ‫ﻘﻮط‬‫ﺳ‬ ‫ﺔ‬‫زاوﯾ‬ ‫ان‬ ‫ﺚ‬‫ﺑﺤﯿ‬ ‫ﺔ‬‫ﻣﺎﺋﻠ‬ ‫وﺑﺼﻮرة‬ ‫ﻋﺎﻛﺲ‬ ‫ﺳﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻀﻮء‬ ‫ﻘﻂ‬
‫ﺟﺰﺋﻲ‬ ‫ﻣﺴﺘﻘﻄﺐ‬ ‫ﯾﻜﻮن‬ ‫اﻟﻤﻨﻌﻜﺲ‬ ‫اﻟﻀﻮء‬ ‫ﻓﺎن‬.
3-‫ان‬ ‫أي‬ ‫اﻟﻤﺎدي‬ ‫اﻟﻮﺳﻂ‬ ‫ﻓﻲ‬ ‫اﻟﻀﻮء‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫اﻟﻔﺮاغ‬ ‫ﻓﻲ‬ ‫اﻟﻀﻮء‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬) :λ > λn.(
‫ﻣﻌﺎﻣ‬‫اﻟﺤﺮﺟﺔ‬ ‫اﻟﺰاوﯾﺔ‬ ‫ﺟﯿﺐ‬ ‫ﻣﻘﻠﻮب‬ ‫اﻻﻧﻜﺴﺎر‬ ‫ﻞ‬
csin
1
n
θ
=
n:‫ط‬ ‫ﻧﺴﺒﺔ‬‫ﻮل‬‫اﻟﻔﺮاغ‬ ‫ﻓﻲ‬ ‫اﻟﻀﻮء‬ ‫ﻣﻮﺟﺔ‬)λ(‫اﻟﻤﺎدي‬ ‫اﻟﻮﺳﻂ‬ ‫ﻓﻲ‬ ‫اﻟﻀﻮء‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬ ‫اﻟﻰ‬)nλ(
ntan p =θ
λ=fc
n
n
λ
λ
=

59. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺨﺎﻣﺲ‬:‫اﻟ‬‫اﻟﻔﻴﺰﻳﺎﺋﻴﺔ‬ ‫ﺒﺼﺮﻳﺎت‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-60-
‫اﻟﺨﺎﻣﺲ‬ ‫اﻟﻔﺼﻞ‬ ‫ﻗﻮاﻧﻴﻦ‬
Cn
P
m
mm
12
sin
1
n,n,tann
msind,
N
W
d
L
y
tan,
d
L
y,
d
L)
2
1
m(
y,
d
Lm
y
2
sind,)
2
1
m(,m,
θ
=
λ
λ
=θ=
λ=θ=
=θ
λ
=∆
λ+
=
λ
=
∆
λ
π
=Φ
θ=∆λ+=∆λ=∆−=∆
l
llllll

60. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺴﺎدس‬:‫اﻟ‬‫اﻟﺤﺪﻳﺜﺔ‬ ‫ﻔﻴﺰﻳﺎء‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-61-
‫اﻻﺳﻮد‬ ‫اﻟﺠﺴﻢ‬:‫ﺟﻤﯿﻊ‬ ‫ﯾﻤﺘﺺ‬ ‫ﻣﺜﺎﻟﻲ‬ ‫ﻧﻈﺎم‬ ‫وھﻮ‬‫اﻹﺷﻌﺎﻋﺎت‬‫ﺼﺪرا‬‫ﻣ‬ ‫ﻮن‬‫ﯾﻜ‬ ‫ﺪﻣﺎ‬‫ﻋﻨ‬ ‫ﺎﻟﻲ‬‫ﻣﺜ‬ ‫ﺸﻊ‬‫ﻣ‬ ‫ﻀﺎ‬‫اﯾ‬ ‫ﻮ‬‫وھ‬ ‫ﻋﻠﯿﮫ‬ ‫اﻟﺴﺎﻗﻄﺔ‬
‫ﻟﻼﺷﻌﺎع‬.
‫اﻟﺠﺴﻢ‬ ‫ﻗﻮاﻧﯿﻦ‬‫اﻷﺳﻮد‬:
1-‫ﺳﺘﻴﻔﺎن‬ ‫ﻗﺎﻧﻮن‬–‫ﺑﻮﻟﺘﺰﻣﺎن‬:‫ﺴﺎﺣﺔ‬‫اﻟﻤ‬ ‫ﺪة‬‫ﻟﻮﺣ‬ ‫ﺔ‬‫ﻟﻠﻄﺎﻗ‬ ‫اﻟﺰﻣﻨﻲ‬ ‫اﻟﻤﻌﺪل‬ ‫ان‬)‫ﺸﺪة‬‫اﻟ‬(‫ﻮد‬‫اﻻﺳ‬ ‫ﺴﻢ‬‫اﻟﺠ‬ ‫ﺸﻌﮭﺎ‬‫ﯾ‬ ‫ﻲ‬‫اﻟﺘ‬‫ﺐ‬‫ﺗﺘﻨﺎﺳ‬
‫ﺗﺤﺖ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬‫ﺔ‬‫اﻟﻤﻄﻠﻘ‬ ‫ﺮارة‬‫اﻟﺤ‬ ‫ﺔ‬‫ﻟﺪرﺟ‬ ‫ﻊ‬‫اﻟﺮاﺑ‬ ‫اﻻس‬ ‫ﻊ‬‫ﻣ‬ ‫ﺎ‬‫طﺮدﯾ‬ ‫ﺐ‬‫ﺗﺘﻨﺎﺳ‬ ‫ﻲ‬‫اﻟﻤﻨﺤﻨ‬ ‫ﺗﺤﺖ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫وان‬ ‫اﻟﻤﻨﺤﻨﻲ‬
)‫اﻟﻤﻄﻠﻖ‬ ‫اﻟﺼﻔﺮ‬ ‫ﻋﺪا‬.(
‫اﻻﺗﻴﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫رﻳﺎﺿﻴﺎ‬ ‫ﺑﻮﻟﺘﺰﻣﺎن‬ ‫ﺳﺘﻴﻔﺎن‬ ‫ﻗﺎﻧﻮن‬ ‫ﻋﻦ‬ ‫وﻳﻌﺒﺮ‬:
‫ﺣﯿﺚ‬:
I:‫اﻹﺷﻌﺎع‬ ‫ﺷﺪة‬‫اﻻﺳﻮد‬ ‫اﻟﺠﺴﻢ‬ ‫ﻣﻦ‬ ‫اﻟﻤﻨﺒﻌﺚ‬‫ﺑﻮﺣﺪة‬)w/m2
.(
T:‫درﺟﺔ‬‫اﻟﻜﻠﻔﻦ‬ ‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﻄﻠﻘﺔ‬ ‫اﻟﺤﺮارة‬َ)K.(
σ:‫ﺳﺘﯿﻔﺎن‬ ‫ﺛﺎﺑﺖ‬–‫ﺣﯿﺚ‬ ‫ﺑﻮﻟﺘﺰﻣﺎن‬)428
K.m/w1067.5 −
×=σ(
2-‫ـﻦ‬‫ـ‬‫ﻟﻔ‬ ‫ـﺔ‬‫ـ‬‫اﻻزاﺣ‬ ‫ـﺎﻧﻮن‬‫ـ‬‫ﻗ‬:‫ذروة‬ ‫ان‬‫ﻮﺟﻲ‬‫اﻟﻤ‬ ‫ﻊ‬‫اﻟﺘﻮزﯾ‬‫ﺴﻢ‬‫اﻟﺠ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺚ‬‫اﻟﻤﻨﺒﻌ‬ ‫ﻌﺎع‬‫ﻟﻼﺷ‬‫ﻮد‬‫اﻷﺳ‬‫ﻮﺟﻲ‬ ‫اﻟﻤ‬ ‫ﻮل‬‫اﻟﻄ‬ ‫ﻮ‬‫ﻧﺤ‬ ‫ﺰاح‬‫ﺗﻨ‬
‫اﻷﻗﺼﺮ‬‫اﻟﻤﻄﻠﻘﺔ‬ ‫اﻟﺤﺮارة‬ ‫درﺟﺔ‬ ‫ارﺗﻔﺎع‬ ‫ﻋﻨﺪ‬)‫ﺗ‬‫ﻋﻜﺴﻲ‬ ‫ﻨﺎﺳﺐ‬(.
‫ﻗﺎﻧﻮن‬ ‫ﻋﻦ‬ ‫وﻳﻌﺒﺮ‬‫ﻟﻔﻦ‬ ‫اﻻزاﺣﺔ‬‫اﻻﺗﻴﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫رﻳﺎﺿﻴﺎ‬:
‫ﺣﯿﺚ‬:
λm:‫اﻟﻤﻘﺎﺑﻞ‬ ‫اﻟﻤﻮﺟﻲ‬ ‫اﻟﻄﻮل‬‫اﺷﻌﺎع‬ ‫ﺷﺪة‬ ‫ﻻﻗﺼﻰ‬)‫اﻟﻤﻘﺎﺑﻞ‬ ‫اﻟﻤﻮﺟﻲ‬ ‫اﻟﻄﻮل‬‫اﻟﻤﻨﺤﻨﻲ‬ ‫ﻟﺬروة‬(‫اﻟﻤﺘﺮ‬ ‫ﺑﻮﺣﺪة‬ ‫وﯾﻘﺎس‬)m(.
T:‫ا‬ ‫ﺑﻮﺣﺪة‬ ‫وﺗﻘﺎس‬ ‫اﻟﻤﺸﻊ‬ ‫ﻟﻠﺠﺴﻢ‬ ‫اﻟﻤﻄﻠﻘﺔ‬ ‫اﻟﺤﺮارة‬ ‫درﺟﺔ‬‫ﻟﻜﻠﻔﻦ‬َ)K(.
‫ﺗﺬﻛﺮ‬:
‫ﺳﻠﻴﺰﻳﺔ‬ ‫درﺟﺔ‬ ‫ﻣﻦ‬ ‫ﻟﻠﺘﺤﻮﻳﻞ‬)ºC(‫ﻣﻄﻠﻘﺔ‬ ‫درﺟﺔ‬ ‫إﻟﻰ‬)T(‫َﻠﻔﻦ‬‫ﻜ‬‫اﻟ‬ ‫ﺑﻮﺣﺪة‬)K(‫اﻵﺗﻴﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻧﺴﺘﺨﺪم‬ ‫ﺑﺎﻟﻌﻜﺲ‬ ‫او‬:
‫ﺑﻼﻧﻚ‬ ‫ﻣﺎﻛﺲ‬ ‫ﻓﺮﺿﻴﺔ‬:‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺴﺘﻘﻠﺔ‬‫وﻣ‬ ‫ﺪدة‬‫ﻣﺤ‬ ‫ﺎت‬‫ﻛﻤ‬ ‫ﻜﻞ‬‫ﺷ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺔ‬‫طﺎﻗ‬ ‫ﺘﺺ‬‫وﯾﻤ‬ ‫ﺸﻊ‬‫ﯾ‬ ‫ان‬ ‫ﻦ‬‫ﯾﻤﻜ‬ ‫ﻮد‬‫اﻻﺳ‬ ‫ﺴﻢ‬‫اﻟﺠ‬ ‫ان‬
‫اﻟﻔﻮﺗﻮﻧﺎت‬ ‫ﺗﺴﻤﻰ‬‫ﻣﻜﻤﺎة‬ ‫ھﻲ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ان‬ ‫ﯾﻌﻨﻲ‬ ‫وھﺬا‬.
‫اﻟﻔﻮﺗﻮن‬ ‫ﻃﺎﻗﺔ‬ ‫ﻓﺎن‬ ‫ﺑﻼﻧﻚ‬ ‫ﻣﺎﻛﺲ‬ ‫ﻓﺮﺿﻴﺔ‬ ‫وﺣﺴﺐ‬)E(‫اﻵﺗﻴﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬ ‫ﺗﻌﻄﻰ‬:
‫اﻻﺷﻌﺎع‬ ‫ﺗﺮدد‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫ﺗﺘﻨﺎﺳﺐ‬ ‫اﻟﻔﻮﺗﻮن‬ ‫طﺎﻗﺔ‬ ‫ان‬ ‫ﯾﻌﻨﻲ‬ ‫ھﺬا‬.
‫ﻓﺎن‬ ‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻴﺔ‬ ‫ﻟﻠﻤﻮﺟﺎت‬ ‫اﻟﻌﺎﻣﺔ‬ ‫اﻟﻤﻌﺎدﻟﺔ‬ ‫وﺣﺴﺐ‬:
λ= fc ⇒
λ
=
c
f
‫اﻟﻔﻮﺗﻮن‬ ‫ﻃﺎﻗﺔ‬ ‫ﺣﺴﺎب‬ ‫ﻳﻤﻜﻦ‬ ‫ﻟﺬﻟﻚ‬‫ﻛﺬﻟﻚ‬‫اﻟﻤﻮﺟﻲ‬ ‫اﻟﻄﻮل‬ ‫ﺑﺪﻻﻟﺔ‬‫ﻳﺎﺗﻲ‬ ‫وﻛﻤﺎ‬:
3
m
3
mm 10898.2T
T
10898.2
T
1 −
−
×=λ⇒
×
=λ⇒αλ∴
44
TITI σ=⇒α∴
273CT +=ο
λ
=
ch
E
fhE =

61. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺴﺎدس‬:‫اﻟ‬‫اﻟﺤﺪﻳﺜﺔ‬ ‫ﻔﻴﺰﻳﺎء‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-62-
‫ﺣﯿﺚ‬:
E:‫اﻟﺠﻮل‬ ‫ﺑﻮﺣﺪة‬ ‫وﺗﻘﺎس‬ ‫اﻟﻔﻮﺗﻮن‬ ‫طﺎﻗﺔ‬)J.(
h:‫ﺗﺴﺎوي‬ ‫وﻗﯿﻤﺘﮫ‬ ‫ﺑﻼﻧﻚ‬ ‫ﺛﺎﺑﺖ‬)h =6.63×10-34
J.s.(
f:‫ﺗﺮدد‬‫اﻻﺷﻌﺎع‬)‫اﻟﻔﻮﺗﻮن‬ ‫ﺗﺮدد‬(‫ﺑﻮﺣﺪ‬ ‫وﯾﻘﺎس‬‫ة‬‫اﻟﮭﺮﺗﺰ‬)Hz(‫ﺣﯿﺚ‬)
sec
1
Hz =(.
c:‫وﺗﺴﺎوي‬ ‫اﻟﻔﺮاغ‬ ‫ﻓﻲ‬ ‫اﻟﻀﻮء‬ ‫ﺳﺮﻋﺔ‬)c=3×108
m/s.(
λ:‫اﻻﺷﻌﺎع‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬)‫اﻟﻔﻮﺗﻮن‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬(‫ﻣﺘﺮ‬ ‫ﺑﻮﺣﺪة‬)m(.
‫ﺟﻬــ‬‫اﻻﻳﻘــﺎف‬ ‫او‬ ‫اﻟﻘﻄــﻊ‬ ‫ﺪ‬:‫ﺎﻣﻊ‬ ‫اﻟﺠ‬ ‫ﻮح‬ ‫ﻟﻠ‬ ‫ﻰ‬ ‫ﯾﻌﻄ‬ ‫ﺎﻟﺐ‬ ‫ﺳ‬ ‫ﺪ‬ ‫ﺟﮭ‬ ‫ﻞ‬ ‫اﻗ‬ ‫ﻮ‬ ‫ھ‬‫ﻮﺋﯿﺔ‬ ‫اﻟﻜﮭﺮوﺿ‬ ‫ﺔ‬ ‫اﻟﺨﻠﯿ‬ ‫ﻲ‬ ‫ﻓ‬‫ﺎ‬ ‫اﻟﺘﯿ‬ ‫ﻞ‬ ‫ﯾﺠﻌ‬ ‫ﺬي‬ ‫واﻟ‬‫ر‬
‫ﺔ‬‫اﻟﻤﻨﺒﻌﺜ‬ ‫ﻀﻮﺋﯿﺔ‬‫اﻟ‬ ‫ﺎت‬‫ﻟﻼﻟﻜﺘﺮوﻧ‬ ‫اﻟﻌﻈﻤﻰ‬ ‫اﻟﺤﺮﻛﯿﺔ‬ ‫ﻟﻠﻄﺎﻗﺔ‬ ‫ﻣﻘﯿﺎس‬ ‫وﯾﻌﺘﺒﺮ‬ ‫ﺻﻔﺮ‬ ‫ﯾﺴﺎوي‬ ‫اﻟﻜﮭﺮوﺿﻮﺋﻲ‬‫ﺪة‬‫ﺷ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺪ‬‫ﯾﻌﺘﻤ‬ ‫وﻻ‬
‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﻀﻮء‬‫ﺑﺎﻟﻔﻮﻟﻂ‬ ‫وﯾﻘﺎس‬.
‫اﻻﺗﻴﺔ‬ ‫اﻟﺮﻳﺎﺿﻴﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬ ‫اﻻﻳﻘﺎف‬ ‫او‬ ‫اﻟﻘﻄﻊ‬ ‫ﺟﻬﺪ‬ ‫ﻳﺤﺴﺐ‬:
‫ﻟﺬﻟﻚ‬‫ﺟﮭ‬ ‫زاد‬ ‫ﻛﻠﻤﺎ‬‫اﻟﻘﻄﻊ‬ ‫ﺪ‬)‫اﻟﺠﺎﻣﻊ‬ ‫اﻟﻠﻮح‬ ‫ﺳﺎﻟﺒﯿﺔ‬ ‫زادت‬(‫ﻮل‬‫ﻟﻠﻮﺻ‬ ‫ﺮ‬‫اﻛﺒ‬ ‫ﺔ‬‫ﺣﺮﻛﯿ‬ ‫ﺔ‬‫طﺎﻗ‬ ‫ﺎج‬‫ﺗﺤﺘ‬ ‫ﻀﻮﺋﯿﺔ‬‫اﻟ‬ ‫ﺎت‬‫اﻻﻟﻜﺘﺮوﻧ‬ ‫ﺎن‬‫ﻓ‬
‫اﻟﺠﺎﻣﻊ‬ ‫اﻟﻠﻮح‬ ‫إﻟﻰ‬.
v‫اﻟﻤﻨﺒﻌﺜ‬ ‫اﻟﻀﻮﺋﻴﺔ‬ ‫ﻟﻼﻟﻜﺘﺮوﻧﺎت‬ ‫اﻟﻌﻈﻤﻰ‬ ‫اﻟﺤﺮﻛﻴﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻋﻦ‬ ‫ﻳﻌﺒﺮ‬‫ﺔ‬‫اﻻﺗﻴﺔ‬ ‫اﻟﺮﻳﺎﺿﻴﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺎت‬:
‫ﺣﯿﺚ‬:
KEmax:‫اﻟﻌ‬ ‫اﻟﺤﺮﻛﯿﺔ‬ ‫اﻟﻄﺎﻗﺔ‬‫اﻟﻤﻨﺒﻌﺚ‬ ‫ﻟﻼﻟﻜﺘﺮون‬ ‫ﻈﻤﻰ‬‫اﻟﺠﻮل‬ ‫ﺑﻮﺣﺪة‬ ‫وﺗﻘﺎس‬)J(.
e:‫اﻟﻜﻮﻟﻮم‬ ‫ﺑﻮﺣﺪة‬ ‫اﻻﻟﻜﺘﺮون‬ ‫ﺷﺤﻨﺔ‬)C(‫ﺣﯿﺚ‬)e=1.6×10-19
C. (
Vs:‫اﻟﻔﻮﻟﻂ‬ ‫ﺑﻮﺣﺪة‬ ‫اﻻﯾﻘﺎف‬ ‫او‬ ‫اﻟﻘﻄﻊ‬ ‫ﺟﮭﺪ‬)V. (
me:‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﻨﺒﻌﺚ‬ ‫اﻻﻟﻜﺘﺮون‬ ‫ﻛﺘﻠﺔ‬)kg(‫ﺣﯿﺚ‬)me=9.11×10-31
kg. (
max
ν:‫ﻟﻼ‬ ‫اﻻﻋﻈﻢ‬ ‫اﻻﻧﻄﻼق‬‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﻨﺒﻌﺜﺔ‬ ‫اﻟﻀﻮﺋﯿﺔ‬ ‫ﻟﻜﺘﺮوﻧﺎت‬)m/s(.
‫ﻣﻼﺣﻈـﺔ‬/‫ﻲ‬‫وھ‬ ‫ﻮل‬‫اﻟﺠ‬ ‫ﺮ‬‫ﻏﯿ‬ ‫ﺮى‬‫اﺧ‬ ‫ﺪة‬‫ﺑﻮﺣ‬ ‫ﺔ‬‫اﻟﻤﻨﺒﻌﺜ‬ ‫ﻀﻮﺋﯿﺔ‬‫اﻟ‬ ‫ﺎت‬‫ﻟﻼﻟﻜﺘﺮوﻧ‬ ‫ﻰ‬‫اﻟﻌﻈﻤ‬ ‫ﺔ‬‫اﻟﺤﺮﻛﯿ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ﺎس‬‫ﺗﻘ‬ ‫ان‬ ‫ﻦ‬‫ﯾﻤﻜ‬
‫اﻻﻟﻜﺘﺮون‬–‫ﻓﻮﻟﻂ‬)eV.(‫ﻛﻞ‬ ‫وان‬:
‫ﻣﻦ‬ ‫ﻟﻠﺘﺤﻮﯾﻞ‬ ‫ﻟﺬﻟﻚ‬:
× )106.1( 19−
×
eV J
÷ )106.1( 19−
×
2
maxemaxsmax m
2
1
)KE(oreVKE ν==
e
KE
V max
s =
1eV=1.6×10-19
J

62. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺴﺎدس‬:‫اﻟ‬‫اﻟﺤﺪﻳﺜﺔ‬ ‫ﻔﻴﺰﻳﺎء‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-63-
‫ﻻ‬ ‫اﻟﻜﻬﺮوﺿﻮﺋﻴﺔ‬ ‫اﻟﻤﻌﺎدﻟﺔ‬‫ﻳ‬‫ﻨﺸﺘﺎﻳﻦ‬:
‫ﻋﺎم‬ ‫ﻓﻲ‬1905‫ا‬ ‫ﺎﻟﻢ‬‫اﻟﻌ‬ ‫اﺳﺘﻄﺎع‬ ‫م‬‫ﯾ‬‫ﺎن‬‫ﺑ‬ ‫ﻚ‬‫ﺑﻼﻧ‬ ‫ﺎﻛﺲ‬‫ﻟﻤ‬ ‫ﻢ‬‫اﻟﻜ‬ ‫ﺔ‬‫ﻧﻈﺮﯾ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺎدا‬‫اﻋﺘﻤ‬ ‫ﻮﺋﯿﺔ‬‫اﻟﻜﮭﺮوﺿ‬ ‫ﺎھﺮة‬‫اﻟﻈ‬ ‫ﺴﺮ‬‫ﯾﻔ‬ ‫ان‬ ‫ﺸﺘﺎﯾﻦ‬‫ﻨ‬
‫ﺪ‬‫واﺣ‬ ‫ﻮن‬‫ﻓﻮﺗ‬ ‫ﺔ‬‫طﺎﻗ‬ ‫ﺘﺺ‬‫ﯾﻤ‬ ‫اﻟﻜﺘﺮون‬ ‫ﻛﻞ‬ ‫وان‬ ‫ﻓﻮﺗﻮﻧﺎت‬ ‫ﺑﺸﻜﻞ‬ ‫اﻟﻤﻌﺪن‬ ‫ﻋﻠﻰ‬ ‫ﯾﺴﻘﻂ‬ ‫اﻟﻀﻮء‬)E(‫ﺔ‬‫داﻟ‬ ‫ﺪاره‬‫ﻣﻘ‬ ‫ﻐﻼ‬‫ﺷ‬ ‫ﺰ‬‫ﯾﻨﺠ‬ ‫ﻢ‬‫ﺛ‬
‫اﻟﺸﻐﻞ‬)w(‫ارﺗﺒﺎط‬ ‫ﻟﻔﻚ‬‫ﺗﺴﺎوي‬ ‫واﻟﺘﻲ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫وﺑﻘﯿﺔ‬ ‫ﺑﺎﻟﻤﻌﺪن‬ ‫ﮫ‬)E – W(‫ﺣﺮﻛﯿﺔ‬ ‫طﺎﻗﺔ‬ ‫ﺑﺸﻜﻞ‬ ‫ﺗﻈﮭﺮ‬.
‫اﻟﺮﻳﺎﺿـﻴﺔ‬ ‫ﺑﺎﻟﻌﻼﻗـﺔ‬ ‫اﻟﻤﻨﺒﻌﺜـﺔ‬ ‫اﻟـﻀﻮﺋﻴﺔ‬ ‫ﻟﻼﻟﻜﺘﺮوﻧـﺎت‬ ‫اﻟﻌﻈﻤـﻰ‬ ‫اﻟﺤﺮﻛﻴـﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻋﻦ‬ ‫ﻳﻌﺒﺮ‬ ‫اﻳﻨﺸﺘﺎﻳﻦ‬ ‫ﺗﻔﺴﻴﺮ‬ ‫وﺣﺴﺐ‬ ‫ﻟﺬﻟﻚ‬
‫اﻻﺗﻴﺔ‬:
‫ﺣﯿﺚ‬:
KEmax:‫اﻟﻤ‬ ‫ﻟﻼﻟﻜﺘﺮون‬ ‫اﻟﻌﻈﻤﻰ‬ ‫اﻟﺤﺮﻛﯿﺔ‬ ‫اﻟﻄﺎﻗﺔ‬‫ﺟﻮل‬ ‫ﺑﻮﺣﺪة‬ ‫ﻨﺒﻌﺚ‬)J(‫او‬)ev.(
2
maxemaxsmax m
2
1
KEoreVKE ν== )‫ﺟﻮل‬ ‫ﺑﻮﺣﺪة‬(
E:‫ﺟﻮل‬ ‫ﺑﻮﺣﺪة‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﻔﻮﺗﻮن‬ ‫طﺎﻗﺔ‬)J(‫او‬)ev. (
λ
==
hc
EorhfE )‫ﺟﻮل‬ ‫ﺑﻮﺣﺪة‬(
w:‫ﻟﻠﻤﻌﺪن‬ ‫اﻟﺸﻐﻞ‬ ‫داﻟﺔ‬)‫اﻟﻜﺘﺮ‬ ‫ﺑﻀﻌﺔ‬ ‫ﺑﺤﺪود‬ ‫وﻗﯿﻤﺘﮭﺎ‬ ‫ﺑﺎﻟﻤﻌﺪن‬ ‫اﻻﻟﻜﺘﺮون‬ ‫ﺑﮭﺎ‬ ‫ﯾﺮﺗﺒﻂ‬ ‫طﺎﻗﺔ‬ ‫اﻗﻞ‬ ‫وھﻲ‬‫ون‬–‫ﻓﻮﻟﻂ‬)eV(.
ο
ο
λ
==
hc
worhfw
‫ان‬ ‫اذ‬:
οf:‫ﺔ‬‫اﻟﻌﺘﺒ‬ ‫ﺮدد‬‫ﺗ‬)‫ﻣ‬ ‫ﯿﺔ‬‫ﺧﺎﺻ‬ ‫ﺪ‬‫ﯾﻌ‬ ‫ﻮ‬‫وھ‬ ‫ﺪن‬‫اﻟﻤﻌ‬ ‫ﺬﻟﻚ‬‫ﻟ‬ ‫ﻮﺋﻲ‬‫اﻟﻜﮭﺮوﺿ‬ ‫ﺎث‬‫اﻻﻧﺒﻌ‬ ‫ﺪ‬‫ﯾﻮﻟ‬ ‫ﺴﺎﻗﻂ‬‫اﻟ‬ ‫ﻀﻮء‬‫ﻟﻠ‬ ‫ﺮدد‬‫ﺗ‬ ‫ﻞ‬‫اﻗ‬ ‫ﻮ‬‫وھ‬‫ﺰة‬‫ﻤﯿ‬
‫اﻟﻤﻀﺎء‬ ‫ﻟﻠﻤﻌﺪن‬‫ﺑﺎﻟﮭﺮﺗﺰ‬ ‫وﯾﻘﺎس‬)Hz((.
•‫ﻛ‬ ‫اذا‬ ‫ﺴﺎﻗﻂ‬‫اﻟ‬ ‫ﻀﻮء‬‫اﻟ‬ ‫ﺗﺮدد‬ ‫ان‬ ‫ﻧﺠﺪ‬ ‫اﻟﻌﺘﺒﺔ‬ ‫ﺗﺮدد‬ ‫ﺗﻌﺮﯾﻒ‬ ‫ﻣﻦ‬‫اﻗ‬ ‫ﺎن‬‫اﻟﻜﺘﺮ‬ ‫ﺚ‬‫ﺗﻨﺒﻌ‬ ‫ﻻ‬ ‫ﺔ‬‫اﻟﻌﺘﺒ‬ ‫ﺮدد‬‫ﺗ‬ ‫ﻦ‬‫ﻣ‬ ‫ﻞ‬‫ﻦ‬‫ﻣ‬ ‫ﻮﺋﯿﺔ‬‫ﺿ‬ ‫ﺎت‬‫وﻧ‬
‫ﻣﻌﯿﻦ‬ ‫ﻣﻌﺪن‬ ‫ﺳﻄﺢ‬.
ολ:‫اﻟﻌﺘﺒﺔ‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬)‫ﺪن‬‫ﻣﻌ‬ ‫ﻄﺢ‬‫ﺳ‬ ‫ﻣﻦ‬ ‫اﻟﻀﻮﺋﯿﺔ‬ ‫اﻻﻟﻜﺘﺮوﻧﺎت‬ ‫ﺗﺤﺮﯾﺮ‬ ‫ﯾﺴﺘﻄﯿﻊ‬ ‫اﻟﺴﺎﻗﻂ‬ ‫ﻟﻠﻀﻮء‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬ ‫اطﻮل‬ ‫وھﻮ‬
‫ﻣﻌﯿﻦ‬.(
•‫اطﻮ‬ ‫ﻛﺎن‬ ‫اذا‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﻀﻮء‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬ ‫ان‬ ‫ﻧﺠﺪ‬ ‫اﻟﻌﺘﺒﺔ‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬ ‫ﺗﻌﺮﯾﻒ‬ ‫ﻣﻦ‬‫ﺚ‬‫ﺗﻨﺒﻌ‬ ‫ﻻ‬ ‫ﺔ‬‫ﻟﻠﻌﺘﺒ‬ ‫اﻟﻤﻮﺟﻲ‬ ‫اﻟﻄﻮل‬ ‫ﻣﻦ‬ ‫ل‬
‫ﻦ‬‫ﻣ‬ ‫ﻮل‬‫اﻻط‬ ‫ﺔ‬‫اﻟﻤﻮﺟﯿ‬ ‫ﻮال‬‫اﻻط‬ ‫ان‬ ‫أي‬ ‫ﻣﻌﯿﻦ‬ ‫ﻣﻌﺪن‬ ‫ﺳﻄﺢ‬ ‫ﻣﻦ‬ ‫ﺿﻮﺋﯿﺔ‬ ‫اﻟﻜﺘﺮوﻧﺎت‬)ολ(‫ﻚ‬‫ﯾﻤﺘﻠ‬ ‫ﺪن‬‫ﻣﻌ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺴﺎﻗﻄﺔ‬‫واﻟ‬
‫ﺷﻐﻞ‬ ‫داﻟﺔ‬)w(‫ﺿﻮﺋﯿﺔ‬ ‫اﻟﻜﺘﺮوﻧﺎت‬ ‫اﻧﺒﻌﺎث‬ ‫إﻟﻰ‬ ‫ﺗﺆدي‬ ‫ﻻ‬.
v‫اﻟﻤﻌﺎدﻟ‬ ‫ﺗﺤﺪدﻫﺎ‬ ‫اﻟﻌﺘﺒﺔ‬ ‫ﻣﻮﺟﺔ‬ ‫وﻃﻮل‬ ‫اﻟﻌﺘﺒﺔ‬ ‫ﺗﺮدد‬ ‫ﺑﻴﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ان‬‫ﻳﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻴﺔ‬ ‫ﻟﻠﻤﻮﺟﺎت‬ ‫اﻟﻌﺎﻣﺔ‬ ‫ﺔ‬:
‫ﺗﺬﻛﺮ‬:
‫ﻛﺎن‬ ‫اذا‬:
1-)ο>ff(‫اﻧ‬ ‫ﯾﺤﺼﻞ‬‫ﺻﻔﺮ‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫ﺣﺮﻛﯿﺔ‬ ‫وﺑﻄﺎﻗﺔ‬ ‫ﻟﻼﻟﻜﺘﺮوﻧﺎت‬ ‫ﻛﮭﺮوﺿﻮﺋﻲ‬ ‫ﺒﻌﺎث‬)KEmax >0.(
)ο=ff(‫اﻟﻤ‬ ‫ﺳﻄﺢ‬ ‫ﻣﻦ‬ ‫ﻟﻼﻟﻜﺘﺮوﻧﺎت‬ ‫ﺗﺤﺮﯾﺮ‬ ‫ﯾﺤﺼﻞ‬‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ ‫ﺣﺮﻛﯿﺔ‬ ‫وﺑﻄﺎﻗﺔ‬ ‫ﻌﺪن‬)KEmax=0. (
)ο<ff(‫ﺳﻘﻮطﮫ‬ ‫زﻣﻦ‬ ‫طﺎل‬ ‫او‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﻀﻮء‬ ‫ﺷﺪة‬ ‫زادت‬ ‫ﻣﮭﻤﺎ‬ ‫ﻟﻼﻟﻜﺘﺮوﻧﺎت‬ ‫ﻛﮭﺮوﺿﻮﺋﻲ‬ ‫اﻧﺒﻌﺎث‬ ‫ﯾﺤﺼﻞ‬ ‫ﻻ‬.
2-)ολ<λ(‫ﺻﻔﺮ‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫ﺣﺮﻛﯿﺔ‬ ‫وﺑﻄﺎﻗﺔ‬ ‫ﻟﻼﻟﻜﺘﺮوﻧﺎت‬ ‫ﻛﮭﺮوﺿﻮﺋﻲ‬ ‫اﻧﺒﻌﺎث‬ ‫ﯾﺤﺼﻞ‬)KEmax >0.(
)ολ=λ(‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ ‫ﺣﺮﻛﯿﺔ‬ ‫وﺑﻄﺎﻗﺔ‬ ‫اﻟﻤﻌﺪن‬ ‫ﺳﻄﺢ‬ ‫ﻣﻦ‬ ‫ﻟﻼﻟﻜﺘﺮوﻧﺎت‬ ‫ﺗﺤﺮﯾﺮ‬ ‫ﯾﺤﺼﻞ‬)KEmax=0. (
)ολ>λ(‫ﺳﻘﻮطﮫ‬ ‫زﻣﻦ‬ ‫طﺎل‬ ‫او‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﻀﻮء‬ ‫ﺷﺪة‬ ‫زادت‬ ‫ﻣﮭﻤﺎ‬ ‫ﻟﻼﻟﻜﺘﺮوﻧﺎت‬ ‫ﻛﮭﺮوﺿﻮﺋﻲ‬ ‫اﻧﺒﻌﺎث‬ ‫ﯾﺤﺼﻞ‬ ‫ﻻ‬.
οο λ= fc
wE)KE( max
−= ‫اﻟﻜﻬﺮوﺿﻮﺋﻴﺔ‬ ‫اﻟﻤﻌﺎدﻟﺔ‬

63. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺴﺎدس‬:‫اﻟ‬‫اﻟﺤﺪﻳﺜﺔ‬ ‫ﻔﻴﺰﻳﺎء‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-64-
3-)wE >(‫اﻧﺒﻌﺎث‬ ‫ﯾﺤﺼﻞ‬‫ﺻﻔﺮ‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫ﺣﺮﻛﯿﺔ‬ ‫وﺑﻄﺎﻗﺔ‬ ‫ﻟﻼﻟﻜﺘﺮوﻧﺎت‬ ‫ﻛﮭﺮوﺿﻮﺋﻲ‬)KEmax >0.(
)wE=(‫ﻟﻼﻟﻜﺘﺮوﻧﺎت‬ ‫ﺗﺤﺮﯾﺮ‬ ‫ﯾﺤﺼﻞ‬‫اﻟﻤﻌﺪن‬ ‫ﺳﻄﺢ‬ ‫ﻣﻦ‬‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ ‫ﺣﺮﻛﯿﺔ‬ ‫وﺑﻄﺎﻗﺔ‬)KEmax=0. (
)wE<(‫ﻛﮭﺮوﺿﻮﺋﻲ‬ ‫اﻧﺒﻌﺎث‬ ‫ﯾﺤﺼﻞ‬ ‫ﻻ‬‫ﻟﻼﻟﻜﺘﺮوﻧﺎت‬‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﻀﻮء‬ ‫ﺷﺪة‬ ‫زادت‬ ‫ﻣﮭﻤﺎ‬‫ﺳﻘﻮطﮫ‬ ‫زﻣﻦ‬ ‫طﺎل‬ ‫او‬.
‫س‬/‫ﻟﻠﻔﻮﺗﻮن؟‬ ‫اﻟﻤﺰدوج‬ ‫اﻟﺴﻠﻮك‬ ‫رﯾﺎﺿﯿﺎ‬ ‫ﻓﺴﺮ‬
‫ج‬/
‫ﻓﺎن‬ ‫ﺑﻼﻧﻚ‬ ‫ﻟﻤﺎﻛﺲ‬ ‫اﻟﻜﻢ‬ ‫ﻧﻈﺮﯾﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻋﺘﻤﺎدا‬
E =hf
‫اﻟﻜﺘﻠﺔ‬ ‫ﺑﺘﻜﺎﻓﺆ‬ ‫اﻟﺨﺎﺻﺔ‬ ‫اﻧﺸﺘﺎﯾﻦ‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻋﻠﻰ‬ ‫واﻋﺘﻤﺎدا‬)m(‫ﺑﺎﻟﻄﺎﻗﺔ‬)E(‫اﻟﻄﺎﻗﺔ‬ ‫ﻓﺎن‬)E(‫اﻟﻌﻼﻗﺔ‬ ‫وﻓﻖ‬ ‫ﺗﻌﻄﻰ‬:
E =mc2
‫ﻓﺎن‬ ‫اﻟﺴﺎﺑﻘﺘﯿﻦ‬ ‫اﻟﻌﻼﻗﺘﯿﻦ‬ ‫وﻣﻦ‬
mc2
= hf ⇒ 2
c
fh
m =
‫ﻓﺎن‬ ‫اﻟﺴﺎﺑﻘﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫وﻣﻦ‬ ‫ﻛﺘﻠﺔ‬ ‫ﻟﮫ‬ ‫ﻛﺎﻧﺖ‬ ‫ﻟﻮ‬ ‫ﻛﻤﺎ‬ ‫ﯾﺴﻠﻚ‬ ‫اﻟﻔﻮﺗﻮن‬ ‫ان‬ ‫أي‬
c
fh
mc =
Q
λ
=
c
f
‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬:
c
c
h
mc λ= ⇒
λ
=
h
mc
‫ﻓﺎن‬ ‫وﻣﻨﮭﺎ‬
mc
h
=λ
Q p =mc
‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬
p
h
=λ
‫ﻟﻠﻔﻮﺗﻮن‬ ‫اﻟﻤﺮاﻓﻖ‬ ‫اﻟﻤﻮﺟﻲ‬ ‫اﻟﻄﻮل‬ ‫ﺣﺴﺎب‬:
‫اﻵﺗ‬ ‫ﻟﻠﻌﻼﻗﺎت‬ ‫وﻓﻘﺎ‬ ‫ﯾﺤﺴﺐ‬ ‫ﻟﮫ‬ ‫اﻟﻤﺮاﻓﻖ‬ ‫اﻟﻤﻮﺟﻲ‬ ‫اﻟﻄﻮل‬ ‫ﻓﺎن‬ ‫ﻟﻠﻔﻮﺗﻮن‬ ‫اﻟﻤﺰدوج‬ ‫اﻟﺴﻠﻮك‬ ‫ﺗﻔﺴﯿﺮ‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬‫ﯿﺔ‬:
‫ان‬ ‫اذ‬:
P:‫ﺑﻮﺣﺪة‬ ‫اﻟﻔﻮﺗﻮن‬ ‫زﺧﻢ‬)kg.m/s. (
λ:‫ﺑﻮﺣﺪة‬ ‫ﻟﻠﻔﻮﺗﻮن‬ ‫اﻟﻤﺼﺎﺣﺐ‬ ‫اﻟﻤﻮﺟﻲ‬ ‫اﻟﻄﻮل‬)m. (
‫اﻟﻤﻮﺟﻲ‬ ‫اﻟﻄﻮل‬ ‫ان‬ ‫أي‬)λ(‫اﻟﻔﻮﺗﻮن‬ ‫زﺧﻢ‬ ‫ﻣﻊ‬ ‫ﻋﻜﺴﻴﺎ‬ ‫ﻳﺘﻨﺎﺳﺐ‬ ‫ﻟﻠﻔﻮﺗﻮن‬ ‫اﻟﻤﺼﺎﺣﺐ‬)p.(
P
h
cm
h
=λ⇒=λ

64. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺴﺎدس‬:‫اﻟ‬‫اﻟﺤﺪﻳﺜﺔ‬ ‫ﻔﻴﺰﻳﺎء‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-65-
‫س‬/‫ان‬ ‫اﺛﺒﺖ‬:E =pc
‫ج‬/
E=hf=
λ
hc
Q
p
h
=λ
∴
p
h
hc
E = ⇒ E=pc
‫اﻟﻤﺎدﻳﺔ‬ ‫اﻟﻤﻮﺟﺎت‬:‫ﻣ‬ ‫ﻣﻮﺟﺎت‬ ‫ﻟﯿﺴﺖ‬ ‫وھﻲ‬ ‫اﻟﺠﺴﯿﻤﺎت‬ ‫ﺣﺮﻛﺔ‬ ‫ﺗﺼﺎﺣﺐ‬ ‫ﻣﻮﺟﺎت‬ ‫ھﻲ‬‫ﻛﮭﺮوﻣﻐﻨﺎطﯿﺴﯿﺔ‬ ‫ﻣﻮﺟﺎت‬ ‫او‬ ‫ﯿﻜﺎﻧﯿﻜﯿﺔ‬.
‫د‬ ‫ﻓﺮﺿﻴﺔ‬‫ي‬‫ﺑﺮوﻟﻲ‬:‫ﻧﻈﺎ‬ ‫ﻛﻞ‬ ‫ﻓﻲ‬ ‫ان‬‫ﺗﺮاﻓﻖ‬ ‫ﻣﻮﺟﺎت‬ ‫وﺟﻮد‬ ‫ﻣﻦ‬ ‫ﻻﺑﺪ‬ ‫ﻣﯿﻜﺎﻧﯿﻜﻲ‬ ‫م‬)‫ﺗﺼﺎﺣﺐ‬(‫اﻟﻤﺎدﯾﺔ‬ ‫اﻟﺠﺴﯿﻤﺎت‬ ‫ﺣﺮﻛﺔ‬.
‫د‬ ‫ﻣﻮﺟﺔ‬ ‫ﻃﻮل‬ ‫ﺣﺴﺎب‬‫ي‬‫ﺑﺮوﻟﻲ‬:
‫د‬ ‫اﻓﺘﺮض‬‫ي‬‫ﻮﺟﻲ‬‫اﻟﻤ‬ ‫ﻮل‬‫اﻟﻄ‬ ‫ان‬ ‫ﻲ‬‫ﺑﺮوﻟ‬)λ(‫ﺴﯿﻢ‬‫اﻟﺠ‬ ‫ﺰﺧﻢ‬‫ﺑ‬ ‫ﺮﺗﺒﻂ‬‫ﯾ‬ ‫ﺔ‬‫اﻟﻤﺎدﯾ‬ ‫ﺔ‬‫ﻟﻠﻤﻮﺟ‬)p(‫ﺴﯿﺔ‬‫ﻋﻜ‬ ‫ﺔ‬‫ﺑﻌﻼﻗ‬‫ﺣ‬ ‫ﻲ‬‫ﻓ‬ ‫ﻮ‬‫ھ‬ ‫ﺎ‬‫ﻛﻤ‬‫ﺔ‬‫ﺎﻟ‬
‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اﻟﻔﻮﺗﻮن‬:
‫ﺣﯿﺚ‬:
λ:‫وھﻮ‬ ‫ﺑﺮوﻟﻲ‬ ‫دي‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﺘﺤﺮك‬ ‫ﻟﻠﺠﺴﯿﻢ‬ ‫اﻟﻤﺼﺎﺣﺐ‬ ‫اﻟﻤﻮﺟﻲ‬ ‫اﻟﻄﻮل‬)m(.
P:‫ﺑﻮﺣﺪة‬ ‫اﻟﺠﺴﯿﻢ‬ ‫زﺧﻢ‬)kg.m/sec.(
m:‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﺘﺤﺮك‬ ‫اﻟﺠﺴﯿﻢ‬ ‫ﻛﺘﻠﺔ‬)kg. (
ν:‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﺘﺤﺮك‬ ‫اﻟﺠﺴﯿﻢ‬ ‫ﺳﺮﻋﺔ‬)m/sec(‫ﻣﻌ‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫ﺗﺤﺴﺐ‬ ‫ان‬ ‫ﯾﻤﻜﻦ‬ ‫واﻟﺘﻲ‬‫ﺣﯿﺚ‬ ‫ﻟﻠﺠﺴﯿﻢ‬ ‫اﻟﺤﺮﻛﯿﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺮﻓﺔ‬:
v‫ـﺴﻴﻢ‬‫ـ‬‫ﻟﻠﺠ‬ ‫ـﺎﺋﻲ‬‫ـ‬‫اﻟﺜﻨ‬ ‫ـﺴﻠﻮك‬‫ـ‬‫اﻟ‬ ‫ﻳﺘـﻀﺢ‬ ‫ـﺴﺎﺑﻘﺔ‬‫ـ‬‫اﻟ‬ ‫ـﺔ‬‫ـ‬‫اﻟﻌﻼﻗ‬ ‫ﻣـﻦ‬)‫ـﻮﺟﻲ‬‫ـ‬‫واﻟﻤ‬ ‫اﻟـﺪﻗﺎﺋﻘﻲ‬(‫ـﺔ‬‫ـ‬‫ﻓﺎﻟﺠﻬ‬‫ـﺢ‬‫ـ‬‫ﺗﻮﺿ‬ ‫ـﺔ‬‫ـ‬‫اﻟﻌﻼﻗ‬ ‫ـﻦ‬‫ـ‬‫ﻣ‬ ‫اﻟﻴﻤﻨـﻰ‬
‫ﻣﻔﻬﻮم‬‫اﻟﻜﺘﻠـﺔ‬ ‫ﻟﻮﺟـﻮد‬ ‫اﻟﺠﺴﻴﻢ‬)m(‫اﻟـﺰﺧﻢ‬ ‫ﻟﻮﺟـﻮد‬ ‫او‬)νm(‫ﻣﻔﻬـﻮ‬ ‫ﻓﺘﻮﺿـﺢ‬ ‫اﻟﻴـﺴﺮى‬ ‫اﻟﺠﻬـﺔ‬ ‫اﻣـﺎ‬‫ﻟﻮﺟـﻮد‬ ‫اﻟﻤﻮﺟـﺔ‬ ‫م‬
‫اﻟﻤﻮﺟﻲ‬ ‫اﻟﻄﻮل‬)λ.(
‫ﻟﻬﺎﻳﺰﻧﺒﺮك‬ ‫ﻟﻼﻳﻘﻴﻦ‬ ‫او‬ ‫اﻟﻼدﻗﺔ‬ ‫ﻣﺒﺪأ‬:‫اﻧﯿﺎ‬ ‫ﻧﻘﯿﺲ‬ ‫ان‬ ‫اﻟﻤﺴﺘﺤﯿﻞ‬ ‫ﻣﻦ‬)‫ﻧﻔﺴﮫ‬ ‫اﻟﻮﻗﺖ‬ ‫ﻓﻲ‬(‫ﺰﺧﻢ‬‫اﻟ‬ ‫وﻛﺬﻟﻚ‬ ‫ﺑﺎﻟﻀﺒﻂ‬ ‫اﻟﻤﻮﺿﻊ‬
‫ﻟﺠﺴﯿﻢ‬ ‫ﺑﺎﻟﻀﺒﻂ‬ ‫اﻟﺨﻄﻲ‬.
‫اﻟﺘﺎﻟﻴﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫اﻟﻼدﻗﺔ‬ ‫ﻣﺒﺪأ‬ ‫ﻋﻦ‬ ‫ﻳﻌﺒﺮ‬ ‫ﻟﺬﻟﻚ‬:
2
m
2
1
KE ν=
‫اﻟﻜﻤﻴﺘﻴﻦ‬ ‫اﺣﺪى‬ ‫ﻓﻲ‬ ‫اﻟﺨﻄﺎ‬ ‫او‬ ‫اﻟﻼدﻗﺔ‬ ‫ﻟﺤﺴﺎب‬∆x‫او‬∆Pπ
≥∆∆
4
h
px
ν
=λ⇒=λ
m
h
P
h

65. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺴﺎدس‬:‫اﻟ‬‫اﻟﺤﺪﻳﺜﺔ‬ ‫ﻔﻴﺰﻳﺎء‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-66-
‫اﻗﻞ‬ ‫ﻟﺤﺴﺎب‬ ‫اﻣﺎ‬)‫ادﻧﻰ‬(‫اﻟﻜﻤﻴﺘﻴﻦ‬ ‫ﻻﺣﺪى‬ ‫ﻻدﻗﺔ‬)∆x(‫او‬)∆p(‫اﻟﻼ‬ ‫ﻣﺒﺪأ‬ ‫ﻋﻼﻗﺔ‬ ‫ﻓﺎن‬‫ﺑﺎﻟـﺸﻜﻞ‬ ‫ﺗﻜﺘﺐ‬ ‫ﻟﻬﺎﻳﺰﻧﺒﺮك‬ ‫دﻗﺔ‬
‫اﻟ‬‫ﺘﺎﻟﻲ‬:
‫اﻟﺠﺴﯿﻢ‬ ‫زﺧﻢ‬ ‫ﻣﻘﺪار‬ ‫ان‬ ‫وﺑﻤﺎ‬)p(‫ﻛﺘﻠﺘﮫ‬ ‫اﻟﺬي‬)m(‫واﻧﻄﻼﻗﮫ‬)ν(‫اﻵﺗﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫ﯾﻌﻄﻰ‬:
‫اﻟﺠﺴﯿﻢ‬ ‫زﺧﻢ‬ ‫ﻓﻲ‬ ‫اﻟﻼدﻗﺔ‬ ‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬)∆p(‫اﻵﺗﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫ﺗﻌﻄﻰ‬:
‫ﺣﯿﺚ‬:
∆x:‫ﻓﻲ‬ ‫اﻟﺨﻄﺄ‬ ‫اﯾﻀﺎ‬ ‫وﯾﺴﻤﻰ‬ ‫اﻟﺠﺴﯿﻢ‬ ‫ﻣﻮﺿﻊ‬ ‫ﻗﯿﺎس‬ ‫ﻓﻲ‬ ‫اﻟﻼدﻗﺔ‬‫ﻗﯿﺎس‬‫اﻟﺠﺴﯿﻢ‬ ‫ﻣﻮﺿﻊ‬‫ﺑﻮﺣﺪة‬ ‫وﯾﻘﺎس‬)m(.
∆p:‫اﻟﻼ‬‫دﻗﺔ‬‫اﻟﺠﺴﯿﻢ‬ ‫زﺧﻢ‬ ‫ﻗﯿﺎس‬ ‫ﻓﻲ‬‫ﻓﻲ‬ ‫اﻟﺨﻄﺄ‬ ‫اﯾﻀﺎ‬ ‫وﯾﺴﻤﻰ‬‫ﻗﯿﺎس‬‫ﺑﻮﺣﺪة‬ ‫وﯾﻘﺎس‬ ‫اﻟﺠﺴﯿﻢ‬ ‫زﺧﻢ‬)kg.m/s.(
h:‫وﻣﻘﺪاره‬ ‫ﺑﻼﻧﻚ‬ ‫ﺛﺎﺑﺖ‬)6.63×10-34
J.s.(
ν∆:‫ﻓﻲ‬ ‫اﻟﻼدﻗﺔ‬‫ﻗﯿﺎس‬‫ﻓﻲ‬ ‫اﻟﺨﻄﺄ‬ ‫او‬ ‫اﻟﺠﺴﯿﻢ‬ ‫اﻧﻄﻼق‬‫ﻗﯿﺎس‬‫ﺑﻮﺣﺪة‬ ‫وﯾﻘﺎس‬ ‫اﻟﺠﺴﯿﻢ‬ ‫اﻧﻄﻼق‬)m/s.(
•‫ﻟﮭﺎ‬ ‫اﻟﻼدﻗﺔ‬ ‫ﻣﺒﺪأ‬ ‫ﻋﻼﻗﺔ‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬‫ﯿﻦ‬‫ﺑ‬ ‫ﺴﯿﺔ‬‫ﻋﻜ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ان‬ ‫ﻧﺠﺪ‬ ‫ﯾﺰﻧﺒﺮك‬)∆x(‫و‬)∆p(‫ﺔ‬‫ﻗﯿﻤ‬ ‫ﺖ‬‫ﻛﺎﻧ‬ ‫ﺎ‬‫ﻛﻠﻤ‬ ‫ﮫ‬‫اﻧ‬ ‫أي‬)∆x(
‫ﻗﯿﻤﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫ﺻﻐﯿﺮة‬)∆p(‫ﺻﺤﯿﺢ‬ ‫واﻟﻌﻜﺲ‬ ‫ﻛﺒﯿﺮة‬.‫ﻧﻌﺮﻓﮫ‬ ‫ﻣﺎ‬ ‫ﻗﻞ‬ ‫ﻛﻠﻤﺎ‬ ‫اﻟﻜﻤﯿﺘﯿﻦ‬ ‫ھﺎﺗﯿﻦ‬ ‫اﺣﺪى‬ ‫ﻗﯿﺎس‬ ‫دﻗﺔ‬ ‫ارﺗﻔﻌﺖ‬ ‫ﻓﻜﻠﻤﺎ‬
‫اﻻﺧﺮى‬ ‫اﻟﻜﻤﯿﺔ‬ ‫ﻋﻦ‬.
‫س‬/‫ﮫ‬ ‫ﻛﺘﻠﺘ‬ ‫ﺴﯿﻢ‬ ‫ﻟﺠ‬ ‫ﺔ‬ ‫اﻟﻤﺮاﻓﻘ‬ ‫ﻲ‬‫ﺑﺮوﻟ‬ ‫دي‬ ‫ﺔ‬ ‫ﻣﻮﺟ‬ ‫ﻮل‬ ‫ط‬ ‫ﺎن‬ ‫ﻛ‬ ‫اذا‬)m(‫ﻮ‬ ‫ھ‬)λ(‫ﻓﺎﺛﺒ‬‫ﻰ‬ ‫ﺗﻌﻄ‬ ‫ﺴﯿﻢ‬ ‫ﻟﻠﺠ‬ ‫ﺔ‬ ‫اﻟﺤﺮﻛﯿ‬ ‫ﺔ‬ ‫اﻟﻄﺎﻗ‬ ‫ان‬ ‫ﺖ‬
‫اﻻﺗﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬:2
2
m2
h
KE
λ
=
‫ج‬/
2
m
2
1
KE ν=
ν
=λ
m
h
⇒
λ
=ν
m
h
∴ 22
2
2
m2
mh
)
m
h
(m
2
1
KE
λ
=
λ
×= ⇒ 2
2
m2
h
KE
λ
=
‫ﻟﺤﺴﺎب‬‫ادﻧﻰ‬‫او‬ ‫اﻟﻼدﻗﺔ‬‫ادﻧﻰ‬‫اﻟﻜﻤﻴﺘﻴﻦ‬ ‫اﺣﺪى‬ ‫ﻓﻲ‬ ‫ﺧﻄﺎ‬∆x‫او‬∆Pπ
=∆∆
4
h
px
ν∆=∆ mp
ν= mp

66. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺴﺎدس‬:‫اﻟ‬‫اﻟﺤﺪﻳﺜﺔ‬ ‫ﻔﻴﺰﻳﺎء‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-67-
‫اﻟﺴﺎدس‬ ‫اﻟﻔﺼﻞ‬ ‫ﻗﻮاﻧﻴﻦ‬
ν∆=∆
π
=∆∆
π
≥∆∆
ν
=λ=λ
λ
==
λ
==
λ=λ=ν==−=
+=×=λσ=
ο
ο
οο
−
mP,
4
h
Px,
4
h
px
m
h
,
P
h
hc
WorhFW,
hc
EorhFE
Fc,Fc,m
2
1
KE,eVKE,WEKE
C273T,10898.2T,TI
2
maxemaxsmaxmax
3
m
4

67. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺴﺎﺑﻊ‬:‫اﻟ‬‫اﻟﺼﻠﺒﺔ‬ ‫اﻟﺤﺎﻟﺔ‬ ‫ﻜﺘﺮوﻧﻴﺎت‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-68-
‫ﺍﻟﱰﺍﻧﺰﺳﺘﻮﺭ‬ ‫ﻗﻮﺍﻧﲔ‬‫ﻛﻤﻀﺨﻢ‬:
‫ﻓﺎن‬ ‫اﻟﺘﺮاﻧﺰﺳﺘﻮر‬ ‫ﻓﻲ‬ ‫ﻋﺎﻣﺔ‬ ‫ﺑﺼﻮرة‬‫اﻟﺒﺎﻋﺚ‬ ‫ﺗﯿﺎر‬)IE(‫اﻟﻘﺎﻋﺪة‬ ‫ﺗﯿﺎري‬ ‫ﻣﺠﻤﻮع‬ ‫ﯾﺴﺎوي‬)IB(‫واﻟﺠﺎﻣﻊ‬)IC(.‫ان‬ ‫أي‬:
v‫ﻟﻮ‬ ‫ﻓﻤﺜﻼ‬‫اﻟﻘﺎﻋﺪة‬ ‫ﺗﯿﺎر‬ ‫ﻛﺎن‬IB‫ﺜﻼ‬‫ﻣ‬ ‫ﯾﺴﺎوي‬1%‫ﺚ‬‫اﻟﺒﺎﻋ‬ ‫ﺎر‬‫ﺗﯿ‬ ‫ﻦ‬‫ﻣ‬IE‫ﺎﻣﻊ‬‫اﻟﺠ‬ ‫ﺎر‬‫ﺗﯿ‬ ‫ﺎن‬‫ﻓ‬IC‫ﻮن‬‫ﯾﻜ‬99%‫ﺎر‬‫ﺗﯿ‬ ‫ﻦ‬‫ﻣ‬
‫اﻟﺒﺎﻋﺚ‬IE
‫ان‬ ‫أي‬:
IB = 1% IE ⇒ IC = 99% IE
‫اﻟﺘﻴﺎر‬ ‫رﺑﺢ‬)α: (‫اﻟﺨﺮوج‬ ‫ﺗﯿﺎر‬ ‫ﺑﯿﻦ‬ ‫اﻟﻨﺴﺒﺔ‬ ‫ھﻮ‬)Iout(‫اﻟﺪﺧﻮل‬ ‫ﺗﯿﺎر‬ ‫اﻟﻰ‬)Iin. (‫ان‬ ‫أي‬:
‫اﻟﻔﻮﻟﻄﻴﺔ‬ ‫رﺑﺢ‬)AV: (‫اﻟﺨﺮو‬ ‫ﻓﻮﻟﻄﯿﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻨﺴﺒﺔ‬ ‫ھﻮ‬‫ج‬)Vout(‫اﻟﺪﺧﻮل‬ ‫ﻓﻮﻟﻄﯿﺔ‬ ‫اﻟﻰ‬)Vin. (‫ان‬ ‫أي‬:
‫ﻓﺎن‬ ‫اوم‬ ‫ﻗﺎﻧﻮن‬ ‫وﺣﺴﺐ‬:
‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫رﺑﺢ‬ ‫اﯾﺠﺎد‬ ‫ﯾﻤﻜﻦ‬ ‫ﻛﺬﻟﻚ‬)AV(‫اﻻﺗﻲ‬ ‫اﻟﺮﯾﺎﺿﻲ‬ ‫اﻻﺷﺘﻘﺎق‬ ‫ﻣﻦ‬:
in
out
in
out
inin
outout
V
in
out
V
R
R
I
I
RI
RI
A
V
V
A ×==⇒=Q
‫ﻟﻜﻦ‬:
in
out
I
I
=α
∴
‫اﻟﺨﺮوج‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﻧﺴﺒﺔ‬ ‫ﻓﻲ‬ ‫ﻣﻀﺮوﺑﺎ‬ ‫اﻟﺘﯿﺎر‬ ‫رﺑﺢ‬ ‫ﯾﺴﺎوي‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫رﺑﺢ‬ ‫ان‬ ‫أي‬(Rout)‫اﻟﺪﺧﻮل‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫اﻟﻰ‬)Rin. (
in
out
V
R
R
.A α=
inininoutoutout RIV,R.IV ==
in
out
V
V
V
A =
in
out
I
I
=α
CBE III +=

68. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺴﺎﺑﻊ‬:‫اﻟ‬‫اﻟﺼﻠﺒﺔ‬ ‫اﻟﺤﺎﻟﺔ‬ ‫ﻜﺘﺮوﻧﻴﺎت‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-69-
‫اﻟﻘﺪرة‬ ‫رﺑﺢ‬)G: (‫اﻟﺨﺮوج‬ ‫ﻗﺪرة‬ ‫ﺑﯿﻦ‬ ‫اﻟﻨﺴﺒﺔ‬ ‫ھﻮ‬)Pout(‫اﻟﺪﺧﻮل‬ ‫ﻗﺪرة‬ ‫اﻟﻰ‬)Pin. (‫ان‬ ‫أي‬:
‫ﺣ‬‫ﯿﺚ‬:
‫اﻟﻘﺪرة‬ ‫رﺑﺢ‬ ‫اﯾﺠﺎد‬ ‫ﯾﻤﻜﻦ‬ ‫ﻛﺬﻟﻚ‬)G(‫اﻻﺗﻲ‬ ‫اﻟﺮﯾﺎﺿﻲ‬ ‫اﻻﺷﺘﻘﺎق‬ ‫ﻣﻦ‬:
in
out
in
out
inin
outout
in
out
V
V
.
I
I
VI
VI
P
P
G ===
‫ﻟﻜﻦ‬:
in
out
I
I
=α ,
in
out
V
V
V
A =
∴
‫اﻟﻘﺪر‬ ‫رﺑﺢ‬ ‫ان‬ ‫أي‬‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫رﺑﺢ‬ ‫ﻓﻲ‬ ‫ﻣﻀﺮوﺑﺎ‬ ‫اﻟﺘﯿﺎر‬ ‫رﺑﺢ‬ ‫ﯾﺴﺎوي‬ ‫ة‬.
‫ﻣﻼﺣﻈﺎت‬/
1-‫ﺮوج‬‫اﻟﺨ‬ ‫ﺎر‬‫ﺗﯿ‬ ‫ﺎن‬‫ﻓ‬ ‫اﻟﻤﺴﺎﺋﻞ‬ ‫ﻟﺤﻞ‬)Iout(‫ﺎﻣﻊ‬‫اﻟﺠ‬ ‫ﺎر‬‫ﺗﯿ‬ ‫ﺎ‬‫داﺋﻤ‬ ‫ﻮ‬‫ھ‬)IC(‫ﺚ‬‫ﺑﺎﻋ‬ ‫ذو‬ ‫ﺘﻮر‬‫اﻟﺘﺮاﻧﺰﺳ‬ ‫ﻮن‬‫ﻛ‬ ‫ﻦ‬‫ﻋ‬ ‫ﺮ‬‫اﻟﻨﻈ‬ ‫ﺾ‬‫وﺑﻐ‬
‫اﻟﺪﺧﻮل‬ ‫ﺗﯿﺎر‬ ‫ﺑﯿﻨﻤﺎ‬ ‫ﻣﺸﺘﺮﻛﺔ‬ ‫ﻗﺎﻋﺪة‬ ‫ذو‬ ‫او‬ ‫ﻣﺸﺘﺮك‬)Iin(‫اﻟﻘﺎﻋﺪة‬ ‫ﻛﺎﻧﺖ‬ ‫ﻓﺎذا‬ ‫اﻟﻤﺆرﺿﺔ‬ ‫اﻟﻤﻨﻄﻘﺔ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻌﺘﻤﺪ‬‫ھﻲ‬‫اﻟ‬‫ﻤﺆ‬‫ﻓﺎن‬ ‫رﺿﺔ‬
‫اﻟﺪﺧﻮل‬ ‫ﺗﯿﺎر‬)Iin(‫اﻟﺒﺎﻋﺚ‬ ‫ﺗﯿﺎر‬ ‫ھﻮ‬)IE(‫اﻟﺒﺎﻋﺚ‬ ‫ﻛﺎن‬ ‫اذا‬ ‫اﻣﺎ‬‫ھﻮ‬‫اﻟ‬‫اﻟﺪﺧﻮل‬ ‫ﺗﯿﺎر‬ ‫ﻓﺎن‬ ‫ﻤﺆرض‬)Iin(‫اﻟﻘﺎﻋﺪة‬ ‫ﺗﯿﺎر‬ ‫ھﻮ‬)IB.(
‫ان‬ ‫أي‬:
Iout = IC ‫اﻟﻤﺆرﺿﺔ‬ ‫ﻫﻲ‬ ‫اﻟﻘﺎﻋﺪة‬ ‫ام‬ ‫ﻣﺆرض‬ ‫اﻟﺒﺎﻋﺚ‬ ‫ﻛﻮن‬ ‫ﻋﻦ‬ ‫اﻟﻨﻈﺮ‬ ‫وﺑﻐﺾ‬.
Iin = IE ‫اﻟﻤﺸﺘﺮﻛﺔ‬ ‫اﻟﻘﺎﻋﺪة‬ ‫ذو‬ ‫ﻟﻠﺘﺮاﻧﺰﺳﺘﻮر‬)‫اﻟﻤﺆرﺿﺔ‬.(
Iin = IB ‫اﻟﻤﺸﺘﺮك‬ ‫اﻟﺒﺎﻋﺚ‬ ‫ذو‬ ‫ﻟﻠﺘﺮاﻧﺰﺳﺘﻮر‬)‫اﻟﻤﺆرض‬(.
2-‫اﻟﻮﺣﺪات‬ ‫ﻣﻦ‬ ‫ﻣﺠﺮد‬ ‫ﻋﺪد‬ ‫ھﻮ‬ ‫اﻟﻘﺪرة‬ ‫ورﺑﺢ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ورﺑﺢ‬ ‫اﻟﺘﯿﺎر‬ ‫رﺑﺢ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬)‫وﺣﺪات‬ ‫ﺑﺪون‬. (
VA.G α=
in
2
in
inin
2
ininininin
out
2
out
outout
2
outoutoutoutout
R
V
PorRIPorVIP
R
V
PorRIPorVIp
===
===
in
out
p
P
G =

69. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺴﺎﺑﻊ‬:‫اﻟ‬‫اﻟﺼﻠﺒﺔ‬ ‫اﻟﺤﺎﻟﺔ‬ ‫ﻜﺘﺮوﻧﻴﺎت‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-70-
‫ﺍﻟﻮﺍﺟﺒﺎﺕ‬
‫ﻣﺜﺎل‬1/‫ﺎن‬‫ﻛ‬ ‫اذا‬ ‫ﺸﺘﺮك‬‫اﻟﻤ‬ ‫ﺚ‬‫اﻟﺒﺎﻋ‬ ‫ذي‬ ‫ﺘﻮر‬‫اﻟﺘﺮاﻧﺰﺳ‬ ‫داﺋﺮة‬ ‫ﻓﻲ‬‫ﺚ‬‫اﻟﺒﺎﻋ‬ ‫ﺎر‬‫ﺗﯿ‬480µA‫ﺎﻣﻊ‬‫اﻟﺠ‬ ‫ﺎر‬‫وﺗﯿ‬450µA‫ﺔ‬‫وﻣﻘﺎوﻣ‬
‫اﻟﺨﺮوج‬80kΩ‫اﻟﺪﺧﻮل‬ ‫وﻣﻘﺎوﻣﺔ‬20Ω‫اﺣﺴﺐ‬:
1-‫اﻟﺘﯿﺎر‬ ‫رﺑﺢ‬2-‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫رﺑﺢ‬3-‫اﻟﻘﺪرة‬ ‫رﺑﺢ‬.)‫ج‬/15 , 60000 , 900000(
‫ﻣﺜﺎل‬2/‫ﺔ‬‫اﻟﻔﻮﻟﻄﯿ‬ ‫ﺢ‬‫رﺑ‬ ‫ﻛﺎن‬ ‫اذا‬ ‫اﻟﻤﺸﺘﺮك‬ ‫اﻟﺒﺎﻋﺚ‬ ‫ذي‬ ‫اﻟﺘﺮاﻧﺰﺳﺘﻮر‬ ‫داﺋﺮة‬ ‫ﻓﻲ‬1500‫ﺮوج‬‫اﻟﺨ‬ ‫ﺔ‬‫وﻓﻮﻟﻄﯿ‬294V‫ﺔ‬‫وﻣﻘﺎوﻣ‬
‫اﻟﺪﺧﻮل‬40Ω‫اﻟﺒﺎﻋﺚ‬ ‫وﺗﯿﺎر‬784mA‫اﻟﻘﺪرة‬ ‫رﺑﺢ‬ ‫اﺣﺴﺐ‬.)‫ج‬/238500(
‫ـﺎل‬‫ـ‬‫ﻣﺜ‬3/‫ﺚ‬‫اﻟﺒﺎﻋ‬ ‫ﺎر‬‫ﺗﯿ‬ ‫ﺎن‬‫ﻛ‬ ‫اذا‬ ‫ﺸﺘﺮﻛﺔ‬‫اﻟﻤ‬ ‫ﺪة‬‫اﻟﻘﺎﻋ‬ ‫ذي‬ ‫ﻀﺨﻢ‬ ‫ﻛﻤ‬ ‫ﺘﻮر‬‫اﻟﺘﺮاﻧﺰﺳ‬ ‫ﺮة‬‫داﺋ‬ ‫ﻲ‬‫ﻓ‬80mA‫ﺪة‬ ‫اﻟﻘﺎﻋ‬ ‫ﺎر‬‫وﺗﯿ‬40µA
‫اﺣﺴﺐ‬:
1-‫اﻟﺠﺎﻣﻊ‬ ‫ﺗﯿﺎر‬.2-‫اﻟﺘﯿﺎر‬ ‫رﺑﺢ‬.)‫ج‬/79.96mA , 0.9995(
‫ﻣﺜــﺎل‬4/‫ﺪة‬ ‫اﻟﻘﺎﻋ‬ ‫ﺎر‬ ‫ﺗﯿ‬ ‫ﺎن‬ ‫ﻛ‬ ‫اذا‬ ‫ﺸﺘﺮﻛﺔ‬ ‫اﻟﻤ‬ ‫ﺪة‬ ‫اﻟﻘﺎﻋ‬ ‫ذي‬ ‫ﻀﺨﻢ‬ ‫ﻛﻤ‬ ‫ﺘﻮر‬ ‫اﻟﺘﺮاﻧﺰﺳ‬ ‫ﺮة‬ ‫داﺋ‬ ‫ﻲ‬ ‫ﻓ‬3mA‫ﺎﻣﻊ‬ ‫اﻟﺠ‬ ‫ﺎر‬ ‫وﺗﯿ‬12mA
‫اﻟﺪﺧﻮل‬ ‫وﻣﻘﺎوﻣﺔ‬30Ω‫اﻟﺨﺮوج‬ ‫وﻣﻘﺎوﻣﺔ‬60kΩ‫ﻓﺎﺣﺴﺐ‬:
1-‫اﻟﺘﯿﺎر‬ ‫رﺑﺢ‬2-‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫رﺑﺢ‬3-‫اﻟﻘﺪرة‬ ‫رﺑﺢ‬.)‫ج‬/0.75 , 1500 , 1125(
‫ﻣﺜﺎل‬5/‫اﻟﺘﺮاﻧﺰﺳ‬ ‫ﺮة‬‫داﺋ‬ ‫ﻲ‬‫ﻓ‬‫ﮫ‬‫ﻓﯿ‬ ‫ﺎر‬‫اﻟﺘﯿ‬ ‫ﺢ‬‫رﺑ‬ ‫ﺎن‬‫ﻛ‬ ‫اذا‬ ‫ﺸﺘﺮﻛﺔ‬‫اﻟﻤ‬ ‫ﺪة‬‫اﻟﻘﺎﻋ‬ ‫ذو‬ ‫ﻀﺨﻢ‬‫ﻛﻤ‬ ‫ﺘﻮر‬0.98‫ﺪﺧﻮل‬‫اﻟ‬ ‫ﺔ‬‫وﻣﻘﺎوﻣ‬50Ω
‫اﻟﺨﺮوج‬ ‫وﻣﻘﺎوﻣﺔ‬400kΩ‫اﻟﻘﺪرة‬ ‫ورﺑﺢ‬ ‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫رﺑﺢ‬ ‫اﺣﺴﺐ‬.)‫ج‬/78400 , 76832(
‫ـﺎل‬‫ـ‬‫ﻣﺜ‬6)‫وزاري‬(/‫ﺸﺘﺮﻛﺔ‬‫اﻟﻤ‬ ‫ﺪة‬ ‫اﻟﻘﺎﻋ‬ ‫ذي‬ ‫ﻀﺨﻢ‬‫ﻛﻤ‬ ‫ﺘﻮر‬‫اﻟﺘﺮاﻧﺰﺳ‬ ‫ﺮة‬‫داﺋ‬ ‫ﻲ‬ ‫ﻓ‬)‫ﺔ‬ ‫اﻟﻤﺆرﺿ‬ ‫ﺪة‬‫اﻟﻘﺎﻋ‬(‫ﺎﻣﻊ‬ ‫اﻟﺠ‬ ‫ﺎر‬‫ﺗﯿ‬ ‫ﺎن‬‫ﻛ‬ ‫اذا‬
)IC=1.96×10-3
A(‫اﻟﻘﺎﻋﺪة‬ ‫وﺗﯿﺎر‬)IB=0.04×10-3
A(‫اﻟﻘﺪرة‬ ‫ورﺑﺢ‬)G=490(‫ﺟﺪ‬ ،:
1-‫اﻟﺘﯿﺎر‬ ‫رﺑﺢ‬2-‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫رﺑﺢ‬.)‫ج‬/0.98 , 500(
‫ـﺎل‬‫ـ‬‫ﻣﺜ‬7)‫وزاري‬(/‫ﺴﺎوي‬‫ﯾ‬ ‫ﺚ‬‫اﻟﺒﺎﻋ‬ ‫ﺎر‬‫ﺗﯿ‬ ‫ﺎن‬‫ﻛ‬ ‫اذا‬ ‫ﺸﺘﺮك‬‫اﻟﻤ‬ ‫ﺚ‬‫اﻟﺒﺎﻋ‬ ‫ذي‬ ‫ﺘﻮر‬‫اﻟﺘﺮاﻧﺰﺳ‬ ‫ﺮة‬‫داﺋ‬ ‫ﻲ‬‫ﻓ‬)IE=0.4mA(‫ﺎر‬ ‫وﺗﯿ‬
‫اﻟﻘﺎﻋﺪة‬)IB=40µA(‫وﻣﻘﺎوﻣﺔ‬‫اﻟﺪﺧﻮل‬)Rin=100Ω(‫اﻟﺨﺮوج‬ ‫وﻣﻘﺎوﻣﺔ‬)Rout=50kΩ(‫ﻣﻘﺪار‬ ‫اﺣﺴﺐ‬:
1-‫اﻟﺘﯿﺎر‬ ‫رﺑﺢ‬)α(2-‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫رﺑﺢ‬)AV(3-‫اﻟﻘﺪرة‬ ‫رﺑﺢ‬)G()‫ج‬/9 , 4500 , 40500(
‫ــــﺎل‬‫ـ‬‫ﻣﺜ‬8)‫وزاري‬(/‫ﻣ‬ ‫ان‬ ‫ﺖ‬ ‫ﻋﻠﻤ‬ ‫اذا‬ ، ‫ﺸﺘﺮك‬ ‫اﻟﻤ‬ ‫ﺚ‬ ‫اﻟﺒﺎﻋ‬ ‫ذي‬ ‫ﺘﻮر‬ ‫اﻟﺘﺮاﻧﺰﺳ‬ ‫ﺮة‬ ‫داﺋ‬ ‫ﻲ‬ ‫ﻓ‬‫ﺢ‬ ‫رﺑ‬ ‫ﺪار‬ ‫ﻘ‬‫ﺎر‬ ‫اﻟﺘﯿ‬=9
‫اﻟﻔﻮﻟﻄﯿﺔ‬ ‫ورﺑﺢ‬=4500‫اﻟﺠﺎﻣﻊ‬ ‫وﺗﯿﺎر‬=0.27mA‫ﻣﻘﺪار‬ ‫اﺣﺴﺐ‬ ،:
1-‫اﻟﻘﺎﻋﺪة‬ ‫ﺗﯿﺎر‬2-‫اﻟﺒﺎﻋﺚ‬ ‫ﺗﯿﺎر‬3-‫اﻟﻘﺪرة‬ ‫رﺑﺢ‬.‫ج‬) /0.03mA , 0.3mA , 40500(

70. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎ‬‫ﻣﻦ‬:‫اﻻ‬‫واﻟﻠﻴﺰر‬ ‫اﻟﺬرﻳﺔ‬ ‫ﻃﻴﺎف‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-71-
v‫ﻋﺎﻣﺔ‬ ‫ﺑﺼﻮرة‬‫اﻻﺗﯿﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻣﺴﺘﻮﯾﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺴﺘﻮﯾﯿﻦ‬ ‫أي‬ ‫ﺑﯿﻦ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻓﺮق‬ ‫ﻋﻦ‬ ‫ﯾﻌﺒﺮ‬:
‫ﻓﻮﻟﻂ‬ ‫اﻟﻜﺘﺮون‬ ‫ﺑﻮﺣﺪة‬ ‫او‬ ‫ﺟﻮل‬ ‫ﺑﻮﺣﺪة‬
‫ﺣﯿﺚ‬:
E∆:‫ﯾﻤﺜﻞ‬‫ﺟﻮل‬ ‫ﺑﻮﺣﺪة‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻣﺴﺘﻮﯾﺎت‬ ‫ﻣﻦ‬ ‫ﻣﺴﺘﻮﯾﯿﻦ‬ ‫أي‬ ‫ﺑﯿﻦ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻓﺮق‬)J(‫او‬)eV. (
E2:‫اﻻﻋﻠﻰ‬ ‫اﻟﻤﺴﺘﻮي‬ ‫طﺎﻗﺔ‬)‫اﻟﺘﮭﯿﺞ‬ ‫ﻣﺴﺘﻮي‬(‫ﺑﻮﺣﺪة‬)J(‫او‬)eV. (
E1:‫اﻻوطﺎ‬ ‫اﻟﻤﺴﺘﻮي‬ ‫طﺎﻗﺔ‬)‫اﻻﺳﺘﻘﺮار‬ ‫ﻣﺴﺘﻮي‬ ‫او‬ ‫اﻻرﺿﻲ‬ ‫اﻟﻤﺴﺘﻮي‬(‫ﺟﻮل‬ ‫ﺑﻮﺣﺪة‬)J(‫او‬)eV. (
‫ﻓﺎﻧﮫ‬ ‫ﻟﻠﺬرة‬ ‫ﺑﻮر‬ ‫ﻧﻤﻮذج‬ ‫ﺣﺴﺐ‬:
v‫ﻟﻠﻄﺎﻗﺔ‬ ‫واطﺊ‬ ‫ﻣﺴﺘﻮي‬ ‫ﻣﻦ‬ ‫اﻟﺬرة‬ ‫اﻟﻜﺘﺮون‬ ‫ﯾﻨﺘﻘﻞ‬)‫ﺑ‬ ‫ﯾﺴﻤﻰ‬‫او‬ ‫اﻻرﺿﻲ‬ ‫ﺎﻟﻤﺴﺘﻮي‬‫اﻻﺳﺘﻘﺮ‬ ‫ﻣﺴﺘﻮي‬‫ار‬(‫ﻣﺴﺘﻮي‬ ‫اﻟﻰ‬‫ﻰ‬‫اﻋﻠ‬
‫ﺔ‬‫ﻟﻠﻄﺎﻗ‬)‫ﯿﺞ‬‫اﻟﺘﮭ‬ ‫ﺴﺘﻮي‬‫ﻣ‬ ‫ﺴﻤﻰ‬‫ﯾ‬(‫ﺎ‬‫ﻓﻮﺗﻮﻧ‬ ‫ﺼﺎﺻﮫ‬‫ﺑﺎﻣﺘ‬ ‫ﻚ‬‫وذﻟ‬‫ﮫ‬‫طﺎﻗﺘ‬)hf(‫ﺴﺘﻮﯾﯿﻦ‬‫اﻟﻤ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺴﺎوي‬‫ﯾ‬ ‫ﺪارھﺎ‬‫ﻣﻘ‬
)∆E(‫ﻣﺘﮭﯿﺠﺔ‬ ‫اﻟﺬرة‬ ‫ﺗﺼﺒﺢ‬ ‫ذﻟﻚ‬ ‫وﻋﻨﺪ‬.
v‫ﻮد‬ ‫ﯾﻌ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﺮﻋﺎن‬ ‫ﺳ‬‫ﻦ‬ ‫ﻣ‬ ‫ﺬرة‬ ‫اﻟ‬ ‫ﺮون‬ ‫اﻟﻜﺘ‬‫اﻟ‬‫ﺴﺘﻮي‬ ‫ﻤ‬‫اﻻ‬‫ﻰ‬ ‫ﻋﻠ‬‫ﺔ‬ ‫ﻟﻠﻄﺎﻗ‬)‫ﯿﺞ‬ ‫اﻟﺘﮭ‬ ‫ﺴﺘﻮي‬ ‫ﻣ‬(‫ﺴﺘﻮ‬ ‫ﻣ‬ ‫ﻰ‬ ‫اﻟ‬‫ﻠﻲ‬ ‫اﻻﺻ‬ ‫اه‬
)‫ﻣﺴﺘﻮي‬‫اﻻﺳﺘﻘﺮار‬(‫ﻓﻮﺗﻮﻧﺎ‬ ‫ﻓﯿﺒﻌﺚ‬‫طﺎﻗﺘﮫ‬)hf(‫ﯾ‬ ‫ﻣﻘﺪارھﺎ‬‫ﺴﺘﻮﯾﯿﻦ‬‫اﻟﻤ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ﻓﺮق‬ ‫ﺴﺎوي‬)∆E(‫و‬‫ﻰ‬‫اﻟ‬ ‫ﺬرة‬‫اﻟ‬ ‫ﻮد‬‫ﺗﻌ‬
‫اﻟﺤﺎﻟﺔ‬ ‫ھﺬه‬ ‫ﻓﻲ‬ ‫اﻻﺳﺘﻘﺮار‬ ‫وﺿﻊ‬.
v‫اﻟﻄﺎﻗﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫ﻓﺎن‬ ‫اﻻﻧﺘﻘﺎﻟﯿﻦ‬ ‫ﻛﻼ‬ ‫ﻓﻲ‬)hf(‫اﻟﺬرة‬ ‫ﺗﻤﺘﺼﮭﺎ‬ ‫اﻟﺘﻲ‬)‫ﺴﺘﻮي‬‫ﻣ‬ ‫ﻰ‬‫اﻟ‬ ‫ﻠﻲ‬‫اﻻﺻ‬ ‫ﺴﺘﻮاه‬‫ﻣ‬ ‫ﻦ‬‫ﻣ‬ ‫اﻻﻟﻜﺘﺮون‬ ‫اﻧﺘﻘﺎل‬ ‫ﻋﻨﺪ‬
‫اﻻﻋﻠﻰ‬ ‫اﻟﻄﺎﻗﺔ‬(‫اﻟﺘﻲ‬ ‫او‬‫اﻟﺬرة‬ ‫ﺗﺸﻌﮭﺎ‬)‫ﻠﻲ‬‫اﻻﺻ‬ ‫ﻣﺴﺘﻮاه‬ ‫اﻟﻰ‬ ‫اﻻﻋﻠﻰ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻣﺴﺘﻮي‬ ‫ﻣﻦ‬ ‫اﻻﻟﻜﺘﺮون‬ ‫اﻧﺘﻘﺎل‬ ‫ﻋﻨﺪ‬(‫ﺴﺎوي‬‫ﺗ‬
‫اﻻﺗﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫رﯾﺎﺿﯿﺎ‬ ‫ذﻟﻚ‬ ‫ﻋﻦ‬ ‫وﯾﻌﺒﺮ‬ ‫اﻟﻤﺴﺘﻮﯾﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻓﺮق‬:
(J) ‫ﺟﻮل‬ ‫ﺑﻮﺣﺪة‬
‫ﺗﺬﻛﺮ‬:‫ﻓﺎن‬ ‫اﻟﻜﻬﺮوﻣﻐﻨﺎﻃﻴﺴﻴﺔ‬ ‫ﻟﻠﻤﻮﺟﺎت‬ ‫اﻟﻌﺎﻣﺔ‬ ‫اﻟﻤﻌﺎدﻟﺔ‬ ‫ﺣﺴﺐ‬:
‫ﺣﯿﺚ‬:
∆E:‫ﺟﻮل‬ ‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﺴﺘﻮﯾﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻓﺮق‬)J. (
h:‫ﺣﯿﺚ‬ ‫ﺑﻼﻧﻚ‬ ‫ﺛﺎﺑﺖ‬)h=6.63×10-34
J.sec. (،c:‫اﻟﻀﻮء‬ ‫ﺳﺮﻋﺔ‬)c=3×108
m/sec(
f:‫اﻟﻤﻨﺒﻌﺚ‬ ‫اﻟﻔﻮﺗﻮن‬ ‫ﺗﺮدد‬‫اﻟﺬرة‬ ‫ﻗﺒﻞ‬ ‫ﻣﻦ‬ ‫اﻟﻤﻤﺘﺺ‬ ‫او‬‫ھﺮﺗﺰ‬ ‫ﺑﻮﺣﺪة‬ ‫اﻻﻧﺘﻘﺎل‬ ‫ﻧﺘﯿﺠﺔ‬)Hz(‫ﺣﯿﺚ‬)Hz=1/sec(.
λ:‫اﻟﻔﻮﺗﻮن‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬‫ﻣﺘﺮ‬ ‫ﺑﻮﺣﺪة‬)m. (
v‫ﻓ‬ ‫ﻛﺬﻟﻚ‬‫زاوﯾﺎ‬ ‫زﺧﻤﺎ‬ ‫ﯾﻤﺘﻠﻚ‬ ‫اﻟﻤﺤﺪد‬ ‫ﻣﺪاره‬ ‫ﻓﻲ‬ ‫اﻻﻟﻜﺘﺮون‬ ‫ﺎن‬‫ﻣﻦ‬ ‫ﺻﺤﯿﺤﺔ‬ ‫اﻋﺪادا‬ ‫ﯾﺴﺎوي‬)
π2
h
. (
‫ان‬ ‫أي‬‫ﻟﻼﻟﻜﺘﺮون‬ ‫اﻟﺰاوي‬ ‫اﻟﺰﺧﻢ‬‫اﻟﻤﺤﺪد‬ ‫ﻣﺪاره‬ ‫ﻓﻲ‬‫ﻳ‬‫ﻌ‬‫ﻋﻨﻪ‬ ‫ﺒﺮ‬‫ﺑﺎﻟﻌﻼﻗﺔ‬‫اﻟﺮﻳﺎﺿﻴﺔ‬‫اﻵﺗﻴﺔ‬:
Ln:‫ﺑﻮﺣﺪة‬ ‫اﻟﻤﺪاري‬ ‫اﻟﺰاوي‬ ‫اﻟﺰﺧﻢ‬)J.sec. (
n:‫اﻟﺮﺋﯿﺴﻲ‬ ‫اﻟﻜﻢ‬ ‫ﻋﺪد‬)‫اﻟﻤﺪار‬ ‫رﻗﻢ‬(‫ﺣﯿﺚ‬)n=1,2,3,4,5……... (
‫ﺣﯿﺚ‬:)n=1,2,3,4,5…….(‫اﻟﺮﺋﯿﺲ‬ ‫اﻟﻜﻤﻲ‬ ‫اﻟﻌﺪد‬ ‫وﯾﻤﺜﻞ‬)‫اﻟﻤﺪار‬ ‫رﻗﻢ‬(.
)sec.J1005.1
2
h 34−
×=
π
. (
λ
=
c
f
λ
=∆=∆
hc
EorhfE
12 EEE −=∆
)
2
h
(nLn
π
=

71. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎ‬‫ﻣﻦ‬:‫اﻻ‬‫واﻟﻠﻴﺰر‬ ‫اﻟﺬرﻳﺔ‬ ‫ﻃﻴﺎف‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-72-
‫ﻋﺎﻣﺔ‬ ‫ﻣﻼﺣﻈﺎت‬:
1-‫اﻻرﺿﻲ‬ ‫ﺑﺎﻟﻤﺴﺘﻮي‬ ‫طﺎﻗﺔ‬ ‫اﻗﻞ‬ ‫ﯾﻤﻠﻚ‬ ‫اﻟﺬي‬ ‫اﻟﻤﺴﺘﻮي‬ ‫ﯾﺴﻤﻰ‬)E1.(
2-‫اﻟﻤﺴﺘﻘﺮ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻣﺴﺘﻮي‬ ‫ﻓﻮق‬ ‫اﺧﺮ‬ ‫ﻣﺴﺘﻮي‬ ‫أي‬)‫اﻻرﺿﻲ‬(‫اﻟﺘﮭﯿﺞ‬ ‫ﻣﺴﺘﻮي‬ ‫ﯾﺴﻤﻰ‬)E2.(
3-‫اﻛﺒﺮ‬ ‫طﺎﻗﺘﮭﺎ‬ ‫ﻛﺎﻧﺖ‬ ‫اﻻرﺿﻲ‬ ‫اﻟﻤﺴﺘﻮي‬ ‫ﻋﻦ‬ ‫اﻟﻤﺴﺘﻮﯾﺎت‬ ‫اﺑﺘﻌﺪت‬ ‫ﻛﻠﻤﺎ‬.
4-‫اﻻ‬ ‫ﺣﺎﻟﺔ‬ ‫اﻟﻰ‬ ‫داﺋﻤﺎ‬ ‫ﺗﻤﯿﻞ‬ ‫اﻟﻤﺘﮭﯿﺠﺔ‬ ‫اﻟﺬرة‬‫ﻗﺼﯿﺮة‬ ‫زﻣﻨﯿﺔ‬ ‫ﻣﺪة‬ ‫ﺑﻌﺪ‬ ‫ﻓﺘﻌﻮد‬ ‫ﺳﺘﻘﺮار‬‫اﻻرﺿﻲ‬ ‫اﻟﻤﺴﺘﻮي‬ ‫اﻟﻰ‬.
5-‫طﺎﻟ‬ ‫طﺎﻗﺔ‬ ‫ﺗﺸﻊ‬ ‫ﻻ‬ ‫اﻟﺬرة‬‫ﺮون‬‫اﻻﻟﻜﺘ‬ ‫ﻞ‬‫ﯾﻨﺘﻘ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻣﻦ‬ ‫ﻣﺤﺪدة‬ ‫ﻛﻤﯿﺔ‬ ‫ﺗﺸﻊ‬ ‫وﻟﻜﻨﮭﺎ‬ ‫اﻟﻤﺤﺪد‬ ‫ﻣﺪاره‬ ‫ﻓﻲ‬ ‫اﻻﻟﻜﺘﺮون‬ ‫ﺑﻘﻲ‬ ‫ﻤﺎ‬
‫ﻦ‬‫ﻣ‬ ‫ﺮون‬‫اﻻﻟﻜﺘ‬ ‫ﺎل‬‫اﻧﺘﻘ‬ ‫ﺪ‬‫ﻋﻨ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺪدة‬‫ﻣﺤ‬ ‫ﺔ‬‫ﻛﻤﯿ‬ ‫ﺘﺺ‬‫ﺗﻤ‬ ‫ﺎ‬‫ﺑﯿﻨﻤ‬ ‫ﺎ‬‫اﻻوط‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ﺴﺘﻮي‬‫ﻣ‬ ‫ﻰ‬‫اﻟ‬ ‫اﻻﻋﻠﻰ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻣﺴﺘﻮي‬ ‫ﻣﻦ‬
‫اﻋﻠﻰ‬ ‫طﺎﻗﺔ‬ ‫ﻣﺴﺘﻮي‬ ‫اﻟﻰ‬ ‫واطﺊ‬ ‫طﺎﻗﺔ‬ ‫ﻣﺴﺘﻮي‬.
6-‫اﺳﺘﻔﺪ‬)1eV=1.6×10-19
J(‫ﻟ‬‫ﻟﻠﺘﺤﻮﯾﻞ‬ ‫ﺬﻟﻚ‬:
‫ﺍﻷﺷﻌﺔ‬‫ﺍﻟﺴﻴﻨﻴﺔ‬x- ray:
‫ـﺴﻴﻨﻴﺔ‬‫ـ‬‫اﻟ‬ ‫ـﻌﺔ‬‫ـ‬‫اﻻﺷ‬:‫ﺎ‬ ‫واطﻮاﻟﮭ‬ ‫ﺴﺠﯿﺔ‬ ‫اﻟﺒﻨﻔ‬ ‫ﻮق‬ ‫ﻓ‬ ‫ﻌﺔ‬ ‫اﻻﺷ‬ ‫ﺮدد‬ ‫ﺗ‬ ‫ﻮق‬ ‫ﯾﻔ‬ ‫ﺎ‬ ‫ﺗﺮددھ‬ ‫ﺔ‬ ‫ﻣﺮﺋﯿ‬ ‫ﺮ‬ ‫ﻏﯿ‬ ‫ﺴﯿﺔ‬ ‫ﻛﮭﺮوﻣﻐﻨﺎطﯿ‬ ‫ﺎت‬ ‫ﻣﻮﺟ‬ ‫ﻲ‬ ‫ھ‬
‫ﻧﺤﻮ‬ ‫ﺟﺪا‬ ‫ﻗﺼﯿﺮة‬ ‫اﻟﻤﻮﺟﯿﺔ‬(0.1 – 10)nm‫ﺑﺎﻟﻤﺠﺎ‬ ‫ﺗﺘﺎﺛﺮ‬ ‫ﻻ‬‫دﻗﺎﺋ‬ ‫ﻟﯿﺴﺖ‬ ‫ﻻﻧﮭﺎ‬ ‫واﻟﻤﻐﻨﺎطﯿﺴﯿﺔ‬ ‫اﻟﻜﮭﺮﺑﺎﺋﯿﺔ‬ ‫ﻻت‬‫ﻣﺸﺤﻮﻧﺔ‬ ‫ﻖ‬.
v‫ﺮق‬‫ﻓ‬ ‫ﺴﻠﯿﻂ‬‫ﺗ‬ ‫ﻋﻨﺪ‬‫ﺪ‬‫ﺟﮭ‬‫ﺪاره‬‫ﻣﻘ‬ ‫ﺎل‬‫ﻋ‬)V(‫ﺎﺛﻮد‬‫اﻟﻜ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺎت‬‫اﻻﻟﻜﺘﺮوﻧ‬ ‫ﻞ‬‫ﺗﺘﻌﺠ‬ ‫ﺴﯿﻨﯿﺔ‬‫اﻟ‬ ‫ﻌﺔ‬‫اﻻﺷ‬ ‫ﺪ‬‫ﺗﻮﻟﯿ‬ ‫ﺔ‬‫اﻧﺒﻮﺑ‬ ‫ﻲ‬‫طﺮﻓ‬ ‫ﻰ‬‫ﻋﻠ‬
‫اﻻﻧﻮد‬ ‫ﺑﺎﺗﺠﺎه‬‫وان‬‫اﻟﻜﺎﺛﻮد‬ ‫ﻣﻦ‬ ‫اﻟﻤﻨﺒﻌﺚ‬ ‫ﻟﻼﻟﻜﺘﺮون‬ ‫اﻟﻌﻈﻤﻰ‬ ‫اﻟﺤﺮﻛﯿﺔ‬ ‫اﻟﻄﺎﻗﺔ‬‫ﻋﻨﮭﺎ‬ ‫ﯾﻌﺒﺮ‬‫اﻻﺗﯿﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺎت‬:
‫ﺣﯿﺚ‬:
KEmax:‫ﺑﻮﺣﺪة‬ ‫ﻟﻼﻟﻜﺘﺮون‬ ‫اﻟﻌﻈﻤﻰ‬ ‫اﻟﺤﺮﻛﯿﺔ‬ ‫اﻟﻄﺎﻗﺔ‬)J. (
e:‫ﺣﯿﺚ‬ ‫اﻻﻟﻜﺘﺮون‬ ‫ﺷﺤﻨﺔ‬)e=1.6×10-19
C. (
V:‫ﻓﻮﻟﻂ‬ ‫ﺑﻮﺣﺪة‬ ‫اﻟﺴﯿﻨﯿﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫اﻧﺒﻮﺑﺔ‬ ‫طﺮﻓﻲ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺴﻠﻂ‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬)V. (
me:‫ﺣﯿﺚ‬ ‫اﻻﻟﻜﺘﺮون‬ ‫ﻛﺘﻠﺔ‬)me=9.11×10-31
kg. (
νmax:‫ﺑﻮﺣﺪة‬ ‫اﻻﻟﻜﺘﺮون‬ ‫ﺳﺮﻋﺔ‬)m/sec. (
v‫ﻧﺘﯿﺠﺔ‬‫ﺔ‬‫اﻟﺤﺮﻛﯿ‬ ‫ﮫ‬‫طﺎﻗﺘ‬ ‫ﻊ‬‫ﺟﻤﯿ‬ ‫ﺗﺘﺤﻮل‬ ‫اﻟﻔﻠﺰي‬ ‫ﺑﺎﻟﮭﺪف‬ ‫اﻟﻤﻌﺠﻞ‬ ‫اﻻﻟﻜﺘﺮون‬ ‫ﻻﺻﻄﺪام‬)KEmax(‫ا‬‫ﻲ‬‫ھ‬ ‫ﻌﺎﻋﯿﺔ‬‫اﺷ‬ ‫ﺔ‬‫طﺎﻗ‬ ‫ﻰ‬‫ﻟ‬
‫اﻟﺴﯿﻨﯿﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫ﻓﻮﺗﻮن‬ ‫طﺎﻗﺔ‬)E(.
‫اﻻﻟﻜﺘﺮون‬ ‫اﺻﻄﺪام‬ ‫ﺑﻌﺪ‬ ‫اﻧﮫ‬ ‫أي‬‫ﺑﺎﻟﮭﺪف‬‫ﻓﺎن‬:
× )106.1( 19−
×
eV J
÷ )106.1( 19−
×
EKEmax =
2
maxemaxmax m
2
1
KEoreVKE ν==

72. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎ‬‫ﻣﻦ‬:‫اﻻ‬‫واﻟﻠﻴﺰر‬ ‫اﻟﺬرﻳﺔ‬ ‫ﻃﻴﺎف‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-73-
v‫ان‬‫ﻢ‬‫أﻋﻈ‬‫ﻮن‬‫ﻟﻔﻮﺗ‬ ‫ﺮدد‬‫ﺗ‬‫ﻌﺔ‬‫اﻷﺷ‬‫ﻋ‬ ‫ﻒ‬‫ﯾﺘﻮﻗ‬ ‫ﻮﺟﻲ‬‫ﻣ‬ ‫ﻮل‬‫ط‬ ‫ﺼﺮ‬‫اﻗ‬ ‫او‬ ‫ﺴﯿﻨﯿﺔ‬‫اﻟ‬‫ﺪ‬‫اﻟﺠﮭ‬ ‫ﺮق‬‫ﻓ‬ ‫ﻰ‬‫ﻠ‬)V(‫ﻲ‬‫طﺮﻓ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺴﻠﻂ‬‫اﻟﻤ‬
‫أﻧﺒﻮﺑﺔ‬‫اﻷﺷﻌﺔ‬‫ﻞ‬‫ﯾﻌﺠ‬ ‫واﻟﺬي‬ ‫اﻟﺴﯿﻨﯿﺔ‬‫ﺮون‬‫اﻹﻟﻜﺘ‬‫ﻰ‬‫ﻋﻈﻤ‬ ‫ﺔ‬‫ﺣﺮﻛﯿ‬ ‫ﺔ‬‫طﺎﻗ‬ ‫ﺴﺒﮫ‬‫ﻓﯿﻜ‬)KEmax(‫ﺮدد‬‫ﺗ‬ ‫ﻢ‬‫اﻋﻈ‬ ‫ﻦ‬‫ﻋ‬ ‫ﺮ‬‫ﯾﻌﺒ‬ ‫ﺬﻟﻚ‬‫ﻟ‬
‫اﻻﺗﯿﺔ‬ ‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺎت‬ ‫ﻣﻮﺟﻲ‬ ‫طﻮل‬ ‫اﻗﺼﺮ‬ ‫او‬ ‫اﻟﺴﯿﻨﯿﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫ﻟﻔﻮﺗﻮن‬:
‫ﺎت‬‫ﻟﻠﻤﻮﺟ‬ ‫ﺔ‬‫اﻟﻌﺎﻣ‬ ‫ﺔ‬‫اﻟﻤﻌﺎدﻟ‬ ‫ﻼل‬‫ﺧ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺎ‬‫ﻋﻨﮭ‬ ‫ﺮ‬‫ﯾﻌﺒ‬ ‫ﻮﺟﻲ‬‫ﻣ‬ ‫ﻮل‬‫ط‬ ‫واﻗﺼﺮ‬ ‫اﻟﺴﯿﻨﯿﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫ﻟﻔﻮﺗﻮن‬ ‫ﺗﺮدد‬ ‫اﻋﻈﻢ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫اﻣﺎ‬
‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫اﻟﻜﮭﺮوﻣﻐﻨﺎطﯿﺴﯿﺔ‬:
‫س‬/‫ﻣﻮﺟﻲ‬ ‫طﻮل‬ ‫اﻗﺼﺮ‬ ‫ﻟﺤﺴﺎب‬ ‫ﻋﻼﻗﺔ‬ ‫اﺷﺘﻖ‬‫اﻟﺴﯿﻨﯿﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫ﻟﻔﻮﺗﻮن‬.
‫ج‬/
Ve
hc
c
hVehfVeEKE
min
min
maxmax
=λ∴
λ
=⇒=⇒=
‫ﺗﺎﺛﻴﺮ‬‫ﻛﻮﻣﺒﺘﻦ‬:‫ﺮة‬‫اﻟﺤ‬ ‫ﺎت‬‫اﻻﻟﻜﺘﺮوﻧ‬ ‫ﺎطﺔ‬‫ﺑﻮﺳ‬ ‫ﺴﺘﻄﺎرة‬‫اﻟﻤ‬ ‫ﺴﯿﻨﯿﺔ‬‫اﻟ‬ ‫ﻌﺔ‬‫اﻻﺷ‬ ‫ﺎت‬‫ﻟﻔﻮﺗﻮﻧ‬ ‫ﻮﺟﻲ‬‫اﻟﻤ‬ ‫ﻮل‬‫اﻟﻄ‬ ‫ﻲ‬‫ﻓ‬ ‫اﻟﺰﯾﺎدة‬ ‫ﻣﻘﺪار‬ ‫ان‬
‫اﻻﺳﺘﻄﺎرة‬ ‫زاوﯾﺔ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻌﺘﻤﺪ‬ ‫اﻟﺴﺎﻗﻄﺔ‬ ‫ﻟﻠﻔﻮﺗﻮﻧﺎت‬ ‫اﻟﻤﻮﺟﻲ‬ ‫ﺑﺎﻟﻄﻮل‬ ‫ﻣﻘﺎرﻧﺔ‬ ‫اﻟﮭﺪف‬ ‫ﻟﺬرة‬)θ(‫اﻻﺗﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫وﻓﻖ‬ ‫ﻓﻘﻂ‬:
‫ﺣﯿﺚ‬:
λ∆:‫اﻟﻤﺴﺘﻄﺎر‬ ‫اﻟﻔﻮﺗﻮن‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬ ‫ﻓﻲ‬ ‫اﻟﺰﯾﺎدة‬‫ﻣﺘﺮ‬ ‫ﺑﻮﺣﺪة‬)m.(
−
λ:‫اﻟﻤﺴﺘﻄﺎر‬ ‫اﻟﻔﻮﺗﻮن‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬.
λ:‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﻔﻮﺗﻮن‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬‫ان‬ ‫أي‬ ‫اﻟﺴﯿﻨﯿﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫ﻟﻔﻮﺗﻮن‬ ‫ﻣﻮﺟﻲ‬ ‫طﻮل‬ ‫اﻗﺼﺮ‬ ‫ﯾﻤﺜﻞ‬ ‫واﻟﺬي‬ ‫اﻟﮭﺪف‬ ‫ﻋﻠﻰ‬:
h:‫وﯾﺴﺎوي‬ ‫ﺑﻼﻧﻚ‬ ‫ﺛﺎﺑﺖ‬)6.63×10-34
J.s.(
me:‫وﺗﺴﺎوي‬ ‫اﻻﻟﻜﺘﺮون‬ ‫ﻛﺘﻠﺔ‬)9.11×10-31
kg.(
c:‫وﺗﺴﺎوي‬ ‫اﻟﻀﻮء‬ ‫ﺳﺮﻋﺔ‬)3×108
m/s.(،θ:‫اﻟﻔﻮﺗﻮن‬ ‫اﺳﺘﻄﺎرة‬ ‫زاوﯾﺔ‬.
cm
h
e
:‫ﺣﯿﺚ‬ ‫ﻛﻮﻣﺒﺘﻦ‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬ ‫ﺗﻤﺜﻞ‬) :m1024.0
cm
h 11
e
−
×=.(
Ve
hc
min =λ=λ
minmaxfc λ=
λ−λ=λ∆ −
)cos1(
cm
h
e
θ−=λ∆
eV
hc
min =λ
h
eV
fmax = ‫ﻟﺤﺴﺎب‬‫أﻋﻈﻢ‬‫اﻟﺴﻴﻨﻴﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫ﻟﻔﻮﺗﻮن‬ ‫ﺗﺮدد‬
‫ﻟﺤﺴﺎب‬‫أﻗﺼﺮ‬‫ﻣﻮﺟﻲ‬ ‫ﻃﻮل‬‫اﻟﺴﻴﻨﻴﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫ﻟﻔﻮﺗﻮن‬
‫ﻛﻮﻣﺒﺘﻦ‬ ‫ﻋﻼﻗﺔ‬

73. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎ‬‫ﻣﻦ‬:‫اﻻ‬‫واﻟﻠﻴﺰر‬ ‫اﻟﺬرﻳﺔ‬ ‫ﻃﻴﺎف‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-74-
‫ﻣﻼﺣﻈ‬‫ﺔ‬/
v‫ﺔ‬‫زاوﯾ‬ ‫ﺎن‬‫ﻓ‬ ‫ﻘﻮطﮫ‬‫ﺳ‬ ‫ﻰ‬‫اﻟ‬ ‫ﺎﻛﺲ‬‫ﻣﻌ‬ ‫ﺎه‬‫ﺑﺎﺗﺠ‬ ‫ﻲ‬‫اﻟﻨﻘ‬ ‫ﺖ‬‫اﻟﻜﺮاﻓﯿ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺪف‬‫ھ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﺴﺎﻗﻂ‬‫اﻟ‬ ‫ﺴﯿﻨﯿﺔ‬‫اﻟ‬ ‫ﻌﺔ‬‫اﻻﺷ‬ ‫ﻮن‬‫ﻓﻮﺗ‬ ‫ﺪ‬‫ﯾﺮﺗ‬ ‫ﺪﻣﺎ‬‫ﻋﻨ‬َ
‫ﺗﺴﺎوي‬ ‫اﻻﺳﺘﻄﺎرة‬180°)θ=180°.(
‫ﺑﻮﻟﺘﺰﻣﺎﻥ‬ ‫ﺗﻮﺯﻳﻊ‬‫ﺍﳌﻌﻜﻮﺱ‬ ‫ﻭﺍﻟﺘﻮﺯﻳﻊ‬:
‫ﺑﻮﻟﺘﺰﻣﺎن‬ ‫ﺗﻮزﻳﻊ‬:‫ﺎم‬‫ﻟﻨﻈ‬ ‫ﺎت‬‫اﻻﯾﻮﻧ‬ ‫او‬ ‫ﺎت‬‫اﻟﺠﺰﯾﺌ‬ ‫او‬ ‫اﻟﺬرات‬ ‫ﻣﻌﻈﻢ‬ ‫ان‬‫ذري‬‫ﺴﺘﻮﯾﺎت‬‫اﻟﻤ‬ ‫ﻲ‬‫ﻓ‬ ‫ﻮن‬‫ﺗﻜ‬ ‫ﺮاري‬‫ﺣ‬ ‫ﺰان‬‫اﺗ‬ ‫ﺔ‬‫ﺣﺎﻟ‬ ‫ﻲ‬‫ﻓ‬
‫اﻟﻤﺴﺘﻮﯾ‬ ‫ﻓﻲ‬ ‫ﻣﺘﮭﯿﺠﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻣﻨﮭﺎ‬ ‫ﻗﻠﯿﻠﺔ‬ ‫وﻧﺴﺒﺔ‬ ‫ﻟﻠﻄﺎﻗﺔ‬ ‫اﻟﻮاطﺌﺔ‬‫ﻟﻠﻄﺎﻗﺔ‬ ‫اﻟﻌﻠﯿﺎ‬ ‫ﺎت‬.
‫ﯾﻠﻲ‬ ‫ﻛﻤﺎ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻣﺴﺘﻮﯾﺎت‬ ‫ﻓﻲ‬ ‫اﻟﺠﺰﯾﺌﺎت‬ ‫او‬ ‫اﻟﺬرات‬ ‫ﻟﺘﻮزﯾﻊ‬ ‫ﺑﻮﻟﺘﺰﻣﺎن‬ ‫ﻗﺎﻧﻮن‬ ‫ﻋﻦ‬ ‫وﯾﻌﺒﺮ‬:
‫ﺣﯿﺚ‬:
k:‫وﻣﻘﺪا‬ ‫ﺑﻮﻟﺘﺰﻣﺎن‬ ‫ﺛﺎﺑﺖ‬‫ﯾﺴﺎوي‬ ‫ره‬1.38×10-23
J/°k
T:‫ﺑﺎﻟﻜﻠﻔﻦ‬ ‫اﻟﺤﺮارة‬ ‫درﺟﺔ‬َ)k(.
kT:‫ﺑﺎﻟﺠﻮل‬ ‫اﻟﺤﺮارﯾﺔ‬ ‫اﻟﻄﺎﻗﺔ‬)J.(
N2:‫ﻟﻠﻄﺎﻗﺔ‬ ‫اﻻﻋﻠﻰ‬ ‫اﻟﻤﺴﺘﻮي‬ ‫ﻓﻲ‬ ‫اﻟﺬرات‬ ‫ﻋﺪد‬.
N1:‫ﻟﻠﻄﺎﻗﺔ‬ ‫اﻻوطﺄ‬ ‫اﻟﻤﺴﺘﻮي‬ ‫ﻓﻲ‬ ‫اﻟﺬرات‬ ‫ﻋﺪد‬)‫اﻻرﺿﻲ‬ ‫اﻟﻤﺴﺘﻮي‬.(
E2:‫ﻟﻠﻄﺎﻗﺔ‬ ‫ﻋﺎﻟﻲ‬ ‫ﻣﺴﺘﻮي‬.
E1:‫ﻟﻠﻄﺎﻗﺔ‬ ‫ﻣﺴﺘﻮي‬ ‫اوطﺄ‬.
)E2 – E1(‫ﺑﯿﻦ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻓﺮق‬‫اﻟﻤﺴﺘﻮﯾﯿﻦ‬)ΔE(‫ان‬ ‫أي‬ ‫اﻟﻔﻮﺗﻮن‬ ‫طﺎﻗﺔ‬ ‫ﺗﺴﺎوي‬ ‫واﻟﺘﻲ‬) :ΔE=E2 – E1=hf.(
v‫ﺎ‬‫ﺣﺮارﯾ‬ ‫ﻣﺘﺰن‬ ‫اﻟﻨﻈﺎم‬ ‫ان‬ ‫وﺣﯿﺚ‬)‫ﺔ‬‫اﻟﻐﺮﻓ‬ ‫ﺮارة‬‫ﺣ‬ ‫ﺔ‬‫درﺟ‬ ‫ﺪ‬‫ﻋﻨ‬(‫ﺴﺘﻮﯾﯿﻦ‬‫اﻟﻤ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ﺮق‬‫ﻓ‬ ‫ﺎن‬‫ﻓ‬ ‫ﺬﻟﻚ‬‫ﻟ‬)E∆(‫ﺴﺎوي‬‫ﯾ‬
‫اﻟﺤﺮارﯾﺔ‬ ‫اﻟﻄﺎﻗﺔ‬)kT. (
‫ﺟﻮل‬ ‫ﺑﻮﺣﺪة‬
ΔE:‫اﻟﻤﺴﺘﻮﯾﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻓﺮق‬‫ﺟﻮل‬ ‫ﺑﻮﺣﺪة‬)J(.
°C:‫اﻟﺴﯿﻠﯿﺰﯾﺔ‬ ‫اﻟﺪرﺟﺔ‬.
‫ﻣﻼﺣﻈﺎﺕ‬/
1-‫اﺳﺘﻔﺪ‬:)e -1
=0.37.(
2-‫ﺣﺮارﻳﺎ‬ ‫ﻣﺘﺰن‬ ‫اﻟﻨﻈﺎم‬ ‫ﻳﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﻓﻘﻂ‬ ‫ﺑﻮﻟﺘﺰﻣﺎن‬ ‫ﻗﺎﻧﻮن‬ ‫ﻳﺘﺤﻘﻖ‬)‫اﻟﻐﺮﻓﺔ‬ ‫ﺣﺮارة‬ ‫درﺟﺔ‬ ‫ﻓﻲ‬(‫ﻳﻜـﻮن‬ ‫اﻟﺤﺎﻟـﺔ‬ ‫ﻫـﺬه‬ ‫ﻓـﻲ‬ ‫ﻻن‬
‫او‬ ‫اﻟﺬرات‬ ‫ﻋﺪد‬‫ﻟﻠﻄﺎﻗﺔ‬ ‫اﻻﻋﻠﻰ‬ ‫اﻟﻤﺴﺘﻮي‬ ‫ﻓﻲ‬ ‫اﻟﺠﺰﻳﺌﺎت‬ ‫او‬ ‫اﻟﺬرات‬ ‫ﻋﺪد‬ ‫ﻣﻦ‬ ‫اﻛﺜﺮ‬ ‫اﻻرﺿﻲ‬ ‫اﻟﻤﺴﺘﻮي‬ ‫ﻓﻲ‬ ‫اﻟﺠﺰﻳﺌﺎت‬.
‫ان‬ ‫أي‬:
2-‫ﻋﻨﺪﻣﺎ‬‫ﻻ‬‫اﻟﺬري‬ ‫اﻟﻨﻈﺎم‬ ‫ﻳﻜﻮن‬‫ﺣﺮارﻳﺎ‬ ‫ﻣﺘﺰن‬‫ﻣـﺴﺘﻮﻳﺎت‬ ‫ﻓـﻲ‬ ‫اﻟـﺬرات‬ ‫ﻋـﺪد‬ ‫ﻣـﻦ‬ ‫اﻛﺜـﺮ‬ ‫اﻟﺘﻬـﻴﺞ‬ ‫ﻣـﺴﺘﻮﻳﺎت‬ ‫ﻓـﻲ‬ ‫اﻟﺬرات‬ ‫ﻋﺪد‬
‫ﺗﺴ‬ ‫اﻟﻌﻤﻠﻴﺔ‬ ‫وﻫﺬه‬ ‫اﻟﻮاﻃﺌﺔ‬ ‫اﻟﻄﺎﻗﺔ‬‫ﻤﻰ‬‫ﺑ‬‫اﻟﻤﻌﻜﻮس‬ ‫ﺎﻟﺘﻮزﻳﻊ‬‫ﺑﻮﻟﺘﺰﻣﺎن‬ ‫ﺗﻮزﻳﻊ‬ ‫ﻳﺨﺎﻟﻒ‬ ‫وﻫﻮ‬.‫ان‬ ‫أي‬:
273CT +°=
kTEorkTEE 12 =∆=−
KT
EE
1
2
12
e
N
N
−
−
=
12 NN >
21
NN > ‫اﻟﺤﺮ‬ ‫اﻻﺗﺰان‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬‫اري‬
‫اﻟﻤﻌﻜﻮس‬ ‫ﺑﺎﻟﺘﻮزﻳﻊ‬ ‫اﻟﻌﻤﻠﻴﺔ‬ ‫ﻫﺬه‬ ‫ﺗﺴﻤﻰ‬
‫ﻗﺎﻧﻮن‬‫ﺑﻮﻟﺘﺰﻣﺎن‬

74. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺜﺎ‬‫ﻣﻦ‬:‫اﻻ‬‫واﻟﻠﻴﺰر‬ ‫اﻟﺬرﻳﺔ‬ ‫ﻃﻴﺎف‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-75-
‫اﻟﺜﺎﻣﻦ‬ ‫اﻟﻔﺼﻞ‬ ‫ﻗﻮاﻧﻴﻦ‬
C273T
kTEorkTEE
kT
)EE(
exp
N
N
Ve
ch
,)cos1(
cm
h'
Ve
hc
,fc,
h
Ve
f
m
2
1
KE,eVKE
)
2
h
(nL
hc
EorhfEorEEE
12
12
1
2
e
minminmaxmax
2
maxemaxmax
n
12
+=
=∆=−



 −−
=
=λθ−=λ−λ=λ∆
=λλ==
υ==
π
=
λ
=∆=∆−=∆
‫ﺍﻟﻔﺼﻞ‬ ‫ﻭﺍﺟﺒﺎﺕ‬
‫ﻣﺜﺎل‬1/‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ﺴﺘﻮي‬‫ﻣ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺪروﺟﯿﻦ‬‫اﻟﮭﯿ‬ ‫ذرة‬ ‫ﺮون‬‫اﻟﻜﺘ‬ ‫ﺎل‬‫اﻧﺘﻘ‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﻨﺒﻌﺚ‬ ‫اﻟﻔﻮﺗﻮن‬ ‫ﺗﺮدد‬ ‫ﻣﺎ‬)eV54.0E5 −=(‫ﻰ‬‫إﻟ‬
‫ﻣﺴﺘ‬‫اﻟﻄﺎﻗﺔ‬ ‫ﻮي‬)eV51.1E3 −=(‫؟‬)‫ج‬/0.234×1015
Hz(
‫ﻣﺜﺎل‬2/‫اﻟﺮاﺑﻊ‬ ‫اﻟﻤﺪار‬ ‫ﻓﻲ‬ ‫ﯾﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻟﮭﯿﺪروﺟﯿﻦ‬ ‫ذرة‬ ‫ﻻﻟﻜﺘﺮون‬ ‫اﻟﺰاوي‬ ‫اﻟﺰﺧﻢ‬ ‫اﺣﺴﺐ‬) .‫ج‬/4.2×10-34
J.sec. (
‫ﻣﺜﺎل‬3/‫ﺗﺮددھﺎ‬ ‫ﺳﯿﻨﯿﺔ‬ ‫أﺷﻌﺔ‬ ‫ﻓﻮﻟﺪ‬ ‫اﻟﺴﯿﻨﯿﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫أﻧﺒﻮﺑﺔ‬ ‫ﻓﻲ‬ ‫اﻟﻔﻠﺰي‬ ‫ﺑﺎﻟﮭﺪف‬ ‫اﻟﻜﺘﺮون‬ ‫اﺻﻄﺪم‬(16×1017
Hz)‫ﻣﻘﺪار‬ ‫ﻓﻤﺎ‬
‫اﻟﻤﻌﺠﻞ؟‬ ‫اﻟﺠﮭﺪ‬ ‫ﻓﺮق‬)‫ج‬/6630V(
‫ﻣﺜﺎل‬4/‫ﺑﻔﻮﻟﻄﯿﺔ‬ ‫ﻣﻌﺠﻠﺔ‬ ‫اﻟﻜﺘﺮوﻧﺎت‬ ‫اﺻﻄﺪام‬ ‫ﻣﻦ‬ ‫اﻟﻤﺘﻮﻟﺪة‬ ‫اﻟﺴﯿﻨﯿﺔ‬ ‫ﻟﻸﺷﻌﺔ‬ ‫ﻣﻮﺟﻲ‬ ‫طﻮل‬ ‫اﻗﺼﺮ‬ ‫ﻣﺎ‬(6.63KV)‫؟‬
‫ﻣﺜﺎل‬5/‫ﺴﺎﻗﻂ‬‫اﻟ‬ ‫ﻮن‬‫اﻟﻔﻮﺗ‬ ‫ﺔ‬‫ﻣﻮﺟ‬ ‫ﻮل‬‫ط‬ ‫ﺎن‬‫ﻛ‬ ‫اذا‬ ‫ﻮﻣﺒﺘﻦ‬‫ﻛ‬ ‫ﺄﺛﯿﺮ‬‫ﺗ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺴﺘﻄﺎر‬‫اﻟﻤ‬ ‫اﻟﻔﻮﺗﻮن‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬ ‫ﻣﺎ‬(0.03nm)‫ﺪﻣﺎ‬‫ﻋﻨ‬
‫ﺑ‬ ‫اﻟﻔﻮﺗﻮن‬ ‫ﯾﺮﺗﺪ‬‫ﺳﻘﻮطﮫ؟‬ ‫ﻻﺗﺠﺎه‬ ‫ﻣﻌﺎﻛﺲ‬ ‫ﺎﺗﺠﺎه‬)‫ج‬/m1048.3 11−
×=λ′(
‫ﻣﺜﺎل‬6/‫ﺴﺘﻄﺎر‬‫اﻟﻤ‬ ‫ﻮن‬‫اﻟﻔﻮﺗ‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬ ‫ﻓﻲ‬ ‫اﻟﺤﺎﺻﻠﺔ‬ ‫اﻟﺰﯾﺎدة‬ ‫ﻣﻘﺪار‬ ‫ﻛﺎن‬ ‫اذا‬)‫ﻮﻣﺒﺘﻦ‬‫ﻛ‬ ‫ﺎﺛﯿﺮ‬‫ﺗ‬ ‫ﻲ‬‫ﻓ‬(‫ﺴﺎوي‬‫ﯾ‬1.2×10-12
m
‫؟‬ ‫اﻻﺳﺘﻄﺎرة‬ ‫زاوﯾﺔ‬ ‫ﻣﻘﺪار‬ ‫ﻓﻤﺎ‬)‫ج‬/°=θ 60(

75. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺘﺎﺳﻊ‬:‫اﻟ‬‫اﻟﻨﺴﺒﻴﺔ‬ ‫ﻨﻈﺮﻳﺔ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-76-
‫اﻟﻜﻼﺳﻴﻜﻴﺔ‬ ‫اﻟﻔﻴﺰﻳﺎء‬:‫ﻓﯿﺰﯾﺎء‬ ‫ھﻲ‬‫اﻷﺟﺴﺎم‬‫ﺑﺴﺮع‬ ‫ﺗﺘﺤﺮك‬ ‫اﻟﺘﻲ‬‫ﺳ‬ ‫ﻣﻦ‬ ‫ﺑﻜﺜﯿﺮ‬ ‫اﻗﻞ‬‫ﻀﻊ‬‫ﺗﺨ‬ ‫ﻲ‬‫واﻟﺘ‬ ‫ﺮاغ‬‫اﻟﻔ‬ ‫ﻲ‬‫ﻓ‬ ‫ﻀﻮء‬‫اﻟ‬ ‫ﺮﻋﺔ‬
‫اﻟﻰ‬‫ﻧﯿﻮﺗﻦ‬ ‫ﻗﻮاﻧﯿﻦ‬.
‫اﻟﻨﺴﺒﻴﺔ‬ ‫اﻟﻔﻴﺰﻳﺎء‬:‫ﺗﺨﻀﻊ‬ ‫واﻟﺘﻲ‬ ‫اﻟﻀﻮء‬ ‫ﺳﺮﻋﺔ‬ ‫ﻣﻦ‬ ‫اﻻﻗﺘﺮاب‬ ‫وﻟﻐﺎﯾﺔ‬ ‫ﺟﺪا‬ ‫ﻋﺎﻟﯿﺔ‬ ‫ﺑﺴﺮع‬ ‫ﺗﺘﺤﺮك‬ ‫اﻟﺘﻲ‬ ‫اﻻﺟﺴﺎم‬ ‫ﻓﯿﺰﯾﺎء‬ ‫ھﻲ‬
‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﻨﻈﺮﯾﺔ‬ ‫ﻗﻮاﻧﯿﻦ‬ ‫اﻟﻰ‬.
‫اﻻﺳﻨﺎد‬ ‫اﻃﺎر‬:‫ﻣﻌﯿﻦ‬ ‫زﻣﻦ‬ ‫ﻓﻲ‬ ‫ﻣﺎ‬ ‫ﺣﺪث‬ ‫ﺑﺮﺻﺪ‬ ‫ﻣﺎ‬ ‫ﺷﺨﺺ‬ ‫ﻓﯿﮫ‬ ‫ﯾﻘﻮم‬ ‫اﻟﺬي‬ ‫اﻟﻤﻮﻗﻊ‬ ‫ھﻮ‬.
‫اﻟﻘﺼﻮرﻳﺔ‬ ‫اﻻﺳﻨﺎد‬ ‫اﻃﺮ‬:‫اﻟﺒﻌﺾ‬ ‫ﺑﻌﻀﮭﺎ‬ ‫اﻟﻰ‬ ‫ﻧﺴﺒﺔ‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫اﻻﺟﺴﺎم‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﺘﺤﺮك‬ ‫اطﺮ‬ ‫ھﻲ‬.
‫اﻟﻤﺮاﻗﺐ‬:‫ﺑﺎﻟﻘﯿﺎﺳﺎت‬ ‫وﯾﻘﻮم‬ ‫ﻣﻌﯿﻦ‬ ‫زﻣﻦ‬ ‫ﻓﻲ‬ ‫ﻣﺎ‬ ‫ﺣﺪث‬ ‫ﯾﺮﺻﺪ‬ ‫اﻟﺬي‬ ‫اﻟﺸﺨﺺ‬ ‫ھﻮ‬.
♦‫اﯾﻨﺸﺘﺎﯾﻦ‬ ‫اﻋﺘﻤﺪ‬‫ﻧﻈﺮﯾﺘﮫ‬ ‫ﻓﻲ‬‫ﻟﻮرﻧﺘ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫ﻋﻠﻰ‬‫اﻻﺳﻨﺎد‬ ‫اطﺎري‬ ‫ﺑﯿﻦ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫ﺰ‬)S‫و‬Ś(
♦‫اﻟﺘﺼﺤﯿﺤﻲ‬ ‫اﻟﻌﺎﻣﻞ‬ ‫ﻋﻠﻰ‬ ‫ﻟﻮرﻧﺘﺰ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫ﺗﺴﻤﯿﺔ‬ ‫اطﻠﻘﺖ‬)γ(‫ﻋﻨﮫ‬ ‫ﯾﻌﺒﺮ‬ ‫واﻟﺬي‬‫اﻻﺗﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬:
‫ﺣﯿﺚ‬:
v:‫اﻟﺠﺴﯿﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﺗﻤﺜﻞ‬.
c:‫اﻟﻔﺮاغ‬ ‫ﻓﻲ‬ ‫اﻟﻀﻮء‬ ‫ﺳﺮﻋﺔ‬.
γ:‫ﻛﺎﻣﺎ‬ ‫وﯾﻘﺮأ‬ ‫اﻟﻮﺣﺪات‬ ‫ﻣﻦ‬ ‫ﻣﺠﺮد‬ ‫ﻋﺪد‬ ‫وھﻮ‬ ‫ﻟﻮرﻧﺘﺰ‬ ‫ﻣﻌﺎﻣﻞ‬َ)Gamma.(
‫ﻣﻼﺣﻈﺎت‬/
1-‫ﻟﻮرﻧﺘﺰ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫ﻓﺎن‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫ﻟﻠﻨﻈﺮﯾﺔ‬ ‫وﻓﻘﺎ‬)γ(‫ﻻن‬ ‫ﺎ‬‫داﺋﻤ‬ ‫ﺪ‬‫اﻟﻮاﺣ‬ ‫ﻦ‬‫ﻣ‬ ‫اﻛﺒﺮ‬ ‫ھﻮ‬‫ﺬر‬‫اﻟﺠ‬ ‫ﺖ‬‫ﺗﺤ‬ ‫ﺪار‬‫اﻟﻤﻘ‬)2
2
c
1
ν
−(‫ﻮ‬‫ھ‬
‫اﻟﻮاﺣﺪ‬ ‫ﻣﻦ‬ ‫اﺻﻐﺮ‬.
2-‫ﺎﻛﻦ‬ ‫ﺳ‬ ‫ﺴﻢ‬ ‫اﻟﺠ‬ ‫ﻮن‬ ‫ﯾﻜ‬ ‫ﺪﻣﺎ‬ ‫ﻋﻨ‬)v=0(‫ﻀﻮء‬ ‫اﻟ‬ ‫ﺮﻋﺔ‬ ‫ﺳ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﺮ‬ ‫ﺑﻜﺜﯿ‬ ‫ﻞ‬ ‫اﻗ‬ ‫ﺴﺮﻋﺔ‬ ‫ﺑ‬ ‫ﺮك‬ ‫ﯾﺘﺤ‬ ‫او‬)v<<c(‫ﺎن‬ ‫ﻓ‬)
c
v
(‫ان‬ ‫ﺎ‬ ‫اﻣ‬
‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬)‫اﻟﺴﺎﻛﻦ‬ ‫ﻟﻠﺠﺴﻢ‬(‫اھﻤﺎﻟﮭﺎ‬ ‫ﯾﻤﻜﻦ‬ ‫او‬)‫اﻟﻀﻮء‬ ‫ﺳﺮﻋﺔ‬ ‫ﻣﻊ‬ ‫ﻣﻘﺎرﻧﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻗﻠﯿﻠﺔ‬ ‫ﻟﻼﺟﺴﺎم‬(‫ﺗﺤﺖ‬ ‫اﻟﻤﻘﺪار‬ ‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬
‫اﻟﺠﺬر‬)2
2
c
1
ν
−(‫اﻟﺤﺎﻟﺔ‬ ‫ھﺬه‬ ‫ﻓﻲ‬ ‫واﺣﺪ‬ ‫ﯾﺴﺎوي‬ ‫ﻟﻮرﻧﺘﺰ‬ ‫ﻣﻌﺎﻣﻞ‬ ‫ﻓﺎن‬ ‫وﺑﺎﻟﺘﺎﻟﻲ‬ ‫واﺣﺪ‬ ‫ﯾﺴﺎوي‬)γ=1.(
3-‫وﻟﻐ‬ ‫ﺪا‬‫ﺟ‬ ‫ﺔ‬‫ﻋﺎﻟﯿ‬ ‫ﺴﺮع‬‫ﺑ‬ ‫اﻟﻤﺘﺤﺮﻛﺔ‬ ‫ﻟﻼﺟﺴﺎم‬‫ﺬر‬‫اﻟﺠ‬ ‫ﺖ‬‫ﺗﺤ‬ ‫ﺪار‬‫اﻟﻤﻘ‬ ‫ﺎن‬‫ﻓ‬ ‫ﻀﻮء‬‫اﻟ‬ ‫ﺮﻋﺔ‬‫ﺳ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺮاب‬‫اﻻﻗﺘ‬ ‫ﺔ‬‫ﺎﯾ‬)2
2
c
1
ν
−(
‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬ ‫اﻟﺼﻔﺮ‬ ‫ﻣﻦ‬ ‫ﯾﻘﺘﺮب‬)γ(‫اﻟﻤﺎﻻﻧﮭﺎﯾﺔ‬ ‫ﻣﻦ‬ ‫ﯾﻘﺘﺮب‬.
‫اوﻻ‬:‫اﻟﺰﻣﻦ‬ ‫ﻧﺴﺒﻴﺔ‬)‫اﻟﺰﻣﻦ‬ ‫ﺗﻤﺪد‬ ‫او‬(:
‫ﺳﺎﻛﻦ‬ ‫راﺻﺪ‬ ‫ﻳﺴﺠﻠﻪ‬ ‫اﻟﺬي‬ ‫واﻟﺰﻣﻦ‬ ‫ﻣﺘﺤﺮك‬ ‫راﺻﺪ‬ ‫ﻳﺴﺠﻠﻪ‬ ‫اﻟﺬي‬ ‫اﻟﺰﻣﻦ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ان‬‫ﻳﺎﺗﻲ‬ ‫ﻛﻤﺎ‬ ‫ﺗﻌﻄﻰ‬:
‫اﻟﺰﻣﻦ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻛﺘﺎﺑﺔ‬ ‫ﻳﻤﻜﻦ‬ ‫ﻛﺬﻟﻚ‬‫ﻳﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫ﻛﺎﻣﺎ‬ ‫ﺑﺪﻻﻟﺔ‬ ‫اﻟﻨﺴﺒﻲ‬ ‫واﻟﺰﻣﻦ‬ ‫اﻟﺤﻘﻴﻘﻲ‬:
t = ο
t γ
2
2
c
1
t
t
ν
−
= ο
2
2
c
1
1
ν
−
=γ
‫اﻟﻨﺴﺒﻲ‬ ‫واﻟﺰﻣﻦ‬ ‫اﻟﺤﻘﻴﻘﻲ‬ ‫اﻟﺰﻣﻦ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻌﻼﻗﺔ‬
‫ﻟﻮرﻧﺘﺰ‬ ‫ﻣﻌﺎﻣﻞ‬

76. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺘﺎﺳﻊ‬:‫اﻟ‬‫اﻟﻨﺴﺒﻴﺔ‬ ‫ﻨﻈﺮﻳﺔ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-77-
‫ﺣﯿﺚ‬:
ο
t:‫ﯾ‬ ‫اﻟﺬي‬ ‫اﻟﺤﺪث‬ ‫زﻣﻦ‬‫اﻟﺤﺪث‬ ‫ﺳﺮﻋﺔ‬ ‫ﺑﻨﻔﺲ‬ ‫ﻣﺘﺤﺮك‬ ‫راﺻﺪ‬ ‫ﺴﺠﻠﮫ‬)‫اﻟﻨﺴﺒﻲ‬ ‫اﻟﺰﻣﻦ‬.(
t:‫اﻟﺰ‬‫ﺳﺎﻛﻦ‬ ‫راﺻﺪ‬ ‫ﯾﺴﺠﻠﮫ‬ ‫اﻟﺬي‬ ‫ﻣﻦ‬)‫اﻟﺤﻘﯿﻘﻲ‬ ‫اﻟﺰﻣﻦ‬.(
♦‫راﺻﺪ‬ ‫ﻳﺴﺠﻠﻪ‬ ‫اﻟﺬي‬ ‫اﻟﺤﺪث‬ ‫زﻣﻦ‬‫ﺳﺎﻛﻦ‬‫ﻣﻦ‬ ‫اﻛﺒﺮ‬‫راﺻﺪ‬ ‫ﻳﺴﺠﻠﻪ‬ ‫اﻟﺬي‬ ‫اﻟﺤﺪث‬ ‫زﻣﻦ‬‫اﻟﺤﺪث‬ ‫ﺳﺮﻋﺔ‬ ‫ﺑﻨﻔﺲ‬ ‫ﻣﺘﺤﺮك‬‫أي‬
‫ان‬):ο
> tt(
‫ﺛﺎﻧﻴﺎ‬:‫اﻟﻄﻮل‬ ‫ﻧﺴﺒﻴﺔ‬)‫اﻟﻄﻮل‬ ‫اﻧﻜﻤﺎش‬ ‫او‬(:
‫ﺑ‬ ‫ﻳﻌﻄﻰ‬ ‫ﺳﺎﻛﻦ‬ ‫وﻫﻮ‬ ‫ﺑﻄﻮﻟﻪ‬ ‫ﻣﻘﺎرﻧﺔ‬ ‫اﻟﻤﺘﺤﺮك‬ ‫اﻟﺠﺴﻢ‬ ‫ﻃﻮل‬ ‫ﻣﻘﺪار‬ ‫ان‬‫اﻻﺗﻴﺔ‬ ‫ﺎﻟﻌﻼﻗﺔ‬:
or
‫ﺣﯿﺚ‬:
L:‫اﻟﻤﺘﺤﺮك‬ ‫اﻟﺠﺴﻢ‬ ‫طﻮل‬)‫اﻟﻨﺴﺒﻲ‬ ‫اﻟﻄﻮل‬‫اﻟﻈﺎھﺮي‬ ‫اﻟﻄﻮل‬ ‫او‬.(
ο
L:‫اﻟﺴﺎﻛﻦ‬ ‫اﻟﺠﺴﻢ‬ ‫طﻮل‬)‫اﻟﺤﻘﯿﻘﻲ‬ ‫اﻟﻄﻮل‬.(
‫اﻟ‬ ‫ﻓﺎن‬ ‫اﻟﻮاﺣﺪ‬ ‫ﻣﻦ‬ ‫اﻗﻞ‬ ‫ﻫﻮ‬ ‫اﻟﺠﺬر‬ ‫ﺗﺤﺖ‬ ‫اﻟﻤﻘﺪار‬ ‫ان‬ ‫وﺑﻤﺎ‬‫اﻟﺤﻘﻴﻘـﻲ‬ ‫اﻟﻄـﻮل‬ ‫ﻣـﻦ‬ ‫اﻗﻞ‬ ‫داﺋﻤﺎ‬ ‫ﻳﻜﻮن‬ ‫اﻟﻨﺴﺒﻲ‬ ‫ﻄﻮل‬)LL( ο<
‫ﺳﻜﻮﻧﻪ‬ ‫اﺛﻨﺎء‬ ‫ﻓﻲ‬ ‫ﻣﺎ‬ ‫ﻟﺠﺴﻢ‬ ‫ﻗﻴﺎﺳﻪ‬ ‫ﻳﻤﻜﻦ‬ ‫ﻃﻮل‬ ‫اﻛﺒﺮ‬ ‫ان‬ ‫ﻣﻌﻨﺎه‬ ‫وﻫﺬا‬.
‫ﺛﺎﻟﺜﺎ‬:‫اﻟﻨﺴﺒﻴﺔ‬ ‫اﻟﻜﺘﻠﺔ‬)‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﻊ‬ ‫اﻟﻜﺘﻠﺔ‬ ‫ﺗﻐﻴﺮ‬(:
‫ﺔ‬‫اﻟﻜﺘﻠ‬ ‫ان‬ ‫أي‬ ‫ﺴﺮﻋﺔ‬‫اﻟ‬ ‫دوال‬ ‫ﻦ‬‫ﻣ‬ ‫ﺔ‬‫داﻟ‬ ‫ﺔ‬‫اﻟﻜﺘﻠ‬ ‫ﺎر‬‫اﻋﺘﺒ‬ ‫ﻲ‬‫ھ‬ ‫اﻟﺨﺎﺻﺔ‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﻨﻈﺮﯾﺔ‬ ‫ﻧﺘﺎﺋﺞ‬ ‫ﻣﻦ‬‫ﻲ‬‫ھ‬ ‫ﺎ‬‫واﻧﻤ‬ ‫ﺔ‬‫ﺛﺎﺑﺘ‬ ‫ﺔ‬‫ﻛﻤﯿ‬ ‫ﺴﺖ‬‫ﻟﯿ‬
‫اﻟﻌﻼﻗﺔ‬ ‫وﻓﻖ‬ ‫ﻋﻠﻰ‬ ‫ﻛﺘﻠﺘﮭﺎ‬ ‫ﺗﻐﯿﺮ‬ ‫ﺣﺴﺎب‬ ‫وﯾﻤﻜﻦ‬ ‫ﻟﺴﺮﻋﺘﮭﺎ‬ ‫ﺗﺒﻌﺎ‬ ‫ﻣﺘﻐﯿﺮ‬ ‫ﻣﻘﺪار‬‫اﻵﺗﯿﺔ‬:
or
‫ﺣﯿﺚ‬:
mrel:‫اﻟﺠﺴﻢ‬ ‫ﻛﺘﻠﺔ‬‫ﺑﺴﺮﻋﺔ‬ ‫اﻟﻤﺘﺤﺮك‬v)‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﻜﺘﻠﺔ‬.(
οm:‫اﻟﺠﺴﻢ‬ ‫ﻛﺘﻠﺔ‬‫ﻓ‬‫ﺳﻜﻮن‬ ‫ﺣﺎﻟﺔ‬ ‫ﻲ‬)‫اﻟﺴﻜﻮﻧﯿﺔ‬ ‫اﻟﻜﺘﻠﺔ‬.(
‫ﻓﻌ‬‫ﺴﺒﯿﺔ‬‫اﻟﻨ‬ ‫ﺔ‬‫اﻟﻜﺘﻠ‬ ‫ﻓﺎن‬ ‫اﻟﻀﻮء‬ ‫ﺳﺮﻋﺔ‬ ‫ﻣﻦ‬ ‫ﻗﺮﯾﺒﺔ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻨﺪﻣﺎ‬‫ﺴﻜﻮﻧﯿﺔ‬‫اﻟ‬ ‫ﺔ‬‫اﻟﻜﺘﻠ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺮ‬‫اﻛﺒ‬)ο> mmrel(‫ا‬ ‫أي‬‫ن‬
‫ﯾﺎﺗﻲ‬ ‫ﻟﻤﺎ‬ ‫وﻓﻘﺎ‬ ‫ﺗﺤﺴﺐ‬ ‫ﺑﺎﻟﻜﺘﻠﺔ‬ ‫اﻟﺰﯾﺎدة‬ ‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬ ‫ﺳﺮﻋﺘﮫ‬ ‫ﺑﺰﯾﺎدة‬ ‫ﺗﺰداد‬ ‫اﻟﺠﺴﻢ‬ ‫ﻛﺘﻠﺔ‬:
γ= οmmrel
γ
= οL
L
ο−=∆ mmm rel
2
2rel
c
1
m
m
υ
−
= ο
2
2
c
1LL
ν
−= ο
‫اﻟﻨﺴﺒﻲ‬ ‫واﻟﻄﻮل‬ ‫اﻟﺤﻘﻴﻘﻲ‬ ‫اﻟﻄﻮل‬ ‫ﺑﻴﻦ‬ ‫اﻟﻌﻼﻗﺔ‬
‫اﻟﺴﻜﻮﻧﻴﺔ‬ ‫واﻟﻜﺘﻠﺔ‬ ‫اﻟﻨﺴﺒﻴﺔ‬ ‫اﻟﻜﺘﻠﺔ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻌﻼﻗﺔ‬

77. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺘﺎﺳﻊ‬:‫اﻟ‬‫اﻟﻨﺴﺒﻴﺔ‬ ‫ﻨﻈﺮﻳﺔ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-78-
‫واﻟﻄﺎﻗﺔ‬ ‫اﻟﻜﺘﻠﺔ‬ ‫ﺗﻜﺎﻓﺆ‬:
‫ﻋﻠﻰ‬ ‫واﻟﻄﺎﻗﺔ‬ ‫اﻟﻜﺘﻠﺔ‬ ‫ﺑﺘﻜﺎﻓﺆ‬ ‫واﻟﺨﺎﺻﺔ‬ ‫ﺘﺎﯾﻦ‬ ‫اﯾﻨ‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫ﺗﻨﺺ‬‫ﺔ‬‫ﻓﺎﻟﻄﺎﻗ‬ ‫ﺔ‬‫ھﺎﺋﻠ‬ ‫ﺔ‬‫طﺎﻗ‬ ‫ﻲ‬‫ﯾﻌﻄ‬ ‫ﺔ‬‫اﻟﻜﺘﻠ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺟﺪا‬ ‫ﺿﺌﯿﻼ‬ ‫ﻣﻘﺪارا‬ ‫ان‬
‫ﻦ‬‫ﻣ‬ ‫ﺪا‬‫ﺟ‬ ‫ﺮة‬‫ﻛﺒﯿ‬ ‫ﺔ‬‫ﻛﻤﯿ‬ ‫ﮫ‬‫ﻋﻨ‬ ‫ﺘﺞ‬‫ﯾﻨ‬ ‫ﺎ‬‫ﻣﻤ‬ ‫ﻀﻮء‬‫اﻟ‬ ‫ﺮﻋﺔ‬‫ﺳ‬ ‫ﻊ‬‫ﻣﺮﺑ‬ ‫ﻲ‬‫ﻓ‬ ‫ﺔ‬‫اﻟﻜﺘﻠ‬ ‫ﺬه‬‫ھ‬ ‫ﺿﺮب‬ ‫ﺣﺎﺻﻞ‬ ‫ﺗﺴﺎوي‬ ‫ﻣﻌﯿﻨﺔ‬ ‫ﻛﺘﻠﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻨﺎﺗﺠﺔ‬
‫اﻟﻄﺎﻗﺔ‬.
•‫ﺍﻟﺮﻳﺎﺿﻴﺔ‬ ‫ﺍﻟﺼﻴﻐﺔ‬ ‫ﺍﻥ‬‫ﻫﻲ‬ ‫ﻭﺍﻟﻄﺎﻗﺔ‬ ‫ﺍﻟﻜﺘﻠﺔ‬ ‫ﺑﺘﻜﺎﻓﺆ‬ ‫ﻭﺍﳋﺎﺻﺔ‬ ‫ﺍﻳﻨﺸﺘﺎﻳﻦ‬ ‫ﳌﻌﺎﺩﻟﺔ‬:
‫ﻣﺘﻼزﻣﺎن‬ ‫ﻣﻔﮭﻮﻣﺎن‬ ‫واﻟﻄﺎﻗﺔ‬ ‫اﻟﻜﺘﻠﺔ‬ ‫ان‬ ‫أي‬.
‫راﺑﻌﺎ‬:‫اﻟﺰﺧﻢ‬ ‫ﻧﺴﺒﻴﺔ‬:
‫ان‬‫اﻟﻨﺴﺒﻲ‬ ‫اﻟﺰﺧﻢ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬)Prel(‫اﻟﻜﻼﺳﯿﻜﻲ‬ ‫واﻟﺰﺧﻢ‬)Pcla(‫ﯾﻠﻲ‬ ‫ﻛﻤﺎ‬ ‫رﯾﺎﺿﯿﺎ‬ ‫ﻋﻨﮭﺎ‬ ‫ﯾﻌﺒﺮ‬:
‫ان‬ ‫اذ‬:
,
mrel:، ‫ﻟﻠﺠﺴﻢ‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﻜﺘﻠﺔ‬ο
m:، ‫اﻟﺴﻜﻮﻧﯿﺔ‬ ‫اﻟﺠﺴﻢ‬ ‫ﻛﺘﻠﺔ‬v:‫اﻟﺠﺴﻢ‬ ‫ﺑﮭﺎ‬ ‫ﯾﺘﺤﺮك‬ ‫اﻟﺘﻲ‬ ‫اﻟﺴﺮﻋﺔ‬
Prel:، ‫اﻟﻨﺴﺒﻲ‬ ‫اﻟﺰﺧﻢ‬pcla:‫اﻟﻜﻼﺳﯿﻜﻲ‬ ‫اﻟﺰﺧﻢ‬
‫ﺧﺎ‬‫ﻣﺴﺎ‬:‫اﻟ‬‫ﻟﻠﺠﺴﻴﻢ‬ ‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻨﺴﺒﻴﺔ‬ ‫ﻄﺎﻗﺔ‬:
‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ان‬)Erel(‫اﻟﺴﻜﻮﻧﯿﺔ‬ ‫واﻟﻄﺎﻗﺔ‬)ο
E(‫ﯾﻠﻲ‬ ‫وﻛﻤﺎ‬ ‫رﯾﺎﺿﯿﺎ‬ ‫ﻋﻨﮭﺎ‬ ‫ﯾﻌﺒﺮ‬:
‫اﯾﻨﺸﺘﺎﯾﻦ‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫وﺣﺴﺐ‬‫و‬ ‫اﻟﻜﺘﻠﺔ‬ ‫ﺑﺘﻜﺎﻓﺆ‬ ‫واﻟﺨﺎﺻﺔ‬‫ﻓﺎن‬ ‫اﻟﻄﺎﻗﺔ‬:
,
‫ﺎن‬ ‫ﻓ‬ ‫ﺬﻟﻚ‬ ‫ﻛ‬‫ﺔ‬ ‫اﻟﻜﻠﯿ‬ ‫ﺴﺒﯿﺔ‬ ‫اﻟﻨ‬ ‫ﺔ‬ ‫اﻟﻄﺎﻗ‬)Erel(‫ﺮك‬ ‫اﻟﻤﺘﺤ‬ ‫ﺴﯿﻢ‬ ‫ﻟﻠﺠ‬‫ﺴﺮﻋﺔ‬ ‫ﺑ‬)v(‫ﺴﺒﯿﺔ‬ ‫اﻟﻨ‬ ‫ﺔ‬ ‫اﻟﺤﺮﻛﯿ‬ ‫ﮫ‬ ‫طﺎﻗﺘ‬ ‫ﻊ‬ ‫ﺟﻤ‬ ‫ﻞ‬ ‫ﺣﺎﺻ‬ ‫ﺴﺎوي‬ ‫ﺗ‬
)KErel(‫اﻟﺴﻜﻮﻧﯿﺔ‬ ‫وطﺎﻗﺘﮫ‬)ο
E(‫ان‬ ‫أي‬:
ο+= E)KE(E relrel
2
cmE οο =
2
2rel
c
1
E
E
ν
−
= ο
2
relrel cmE =
ν= relrel mPν= οmPcla
2
2
cla
rel
c
1
P
P
ν
−
=
2
mcE =
‫اﻟﻜﻼﺳﻴﻜﻲ‬ ‫ﺑﺎﻟﺰﺧﻢ‬ ‫اﻟﻨﺴﺒﻲ‬ ‫اﻟﺰﺧﻢ‬ ‫ﻋﻼﻗﺔ‬
‫ﻋﻼ‬‫اﻟﺴﻜﻮﻧﻴﺔ‬ ‫ﺑﺎﻟﻄﺎﻗﺔ‬ ‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻨﺴﺒﻴﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻗﺔ‬

78. ‫اﻟ‬ ‫اﻟﻔﺼﻞ‬‫ﺘﺎﺳﻊ‬:‫اﻟ‬‫اﻟﻨﺴﺒﻴﺔ‬ ‫ﻨﻈﺮﻳﺔ‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-79-
‫اﻟ‬‫اﻟﺤﺮﻛﻴ‬ ‫ﻄﺎﻗﺔ‬‫اﻟﻨﺴﺒﻴﺔ‬ ‫ﺔ‬:
‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺤﺮﻛﯿﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ان‬)KErel(‫ا‬ ‫ﺑﺮھﻨﮭﺎ‬ ‫ﻛﻤﺎ‬‫ﯾ‬‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻔﺮق‬ ‫ﺗﺴﺎوي‬ ‫ﻨﺸﺘﺎﯾﻦ‬)Erel(‫اﻟﻤﺘﺤﺮك‬ ‫ﻟﻠﺠﺴﯿﻢ‬
‫ﺴﺮﻋﺔ‬ ‫ﺑ‬v‫و‬‫ﺴﻜﻮﻧﯿﺔ‬ ‫اﻟ‬ ‫ﮫ‬ ‫طﺎﻗﺘ‬)ο
E(،‫أي‬‫ﺴﺎوي‬ ‫ﺗ‬ ‫ﻻ‬ ‫ﺔ‬ ‫اﻟﺤﺮﻛﯿ‬ ‫ﮫ‬ ‫طﺎﻗﺘ‬ ‫ان‬)2
mv
2
1
(‫اﻟﻤﯿﻜﺎﻧ‬ ‫ﻲ‬ ‫ﻓ‬ ‫ﺎل‬ ‫اﻟﺤ‬ ‫ﻮ‬ ‫ھ‬ ‫ﺎ‬ ‫ﻛﻤ‬‫ﻚ‬ ‫ﯿ‬
‫اﻟﺴﻜﻮﻧﯿﺔ‬ ‫طﺎﻗﺘﮫ‬ ‫ﻣﻨﮭﺎ‬ ‫ﻣﻄﺮوﺣﺎ‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫طﺎﻗﺘﮫ‬ ‫ﺗﺴﺎوي‬ ‫اﻧﮭﺎ‬ ‫ﺑﻞ‬ ‫اﻟﻜﻼﺳﯿﻜﻲ‬،‫ان‬ ‫أي‬:
or
‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺤﺮﻛﯿﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫اﻣﺎ‬)KErel(‫اﻟﺴﻜﻮ‬ ‫وطﺎﻗﺘﮫ‬ ‫ﻟﻠﺠﺴﯿﻢ‬‫ﻧﯿﺔ‬)οE(‫رﯾ‬ ‫ﻋﻨﮭﺎ‬ ‫ﻓﯿﻌﺒﺮ‬‫ﺎﺿﯿﺎ‬‫ﯾﻠﻲ‬ ‫ﻛﻤﺎ‬:
‫س‬/‫اﻟﻌﻼﻗﺔ‬ ‫اﺷﺘﻖ‬:4222
rel
2
rel
cmc)P()E( ο
+=
‫ج‬/
4222
rel
2
rel
4222
rel
42
rel
222
rel
22
rel
22222
rel
222
rel
22
cla
22
rel
22
rel
2
cla2
2
2
rel
2
rel
2
2
2
cla2
rel
2
2
cla
rel
422
rel
2
rel
42222
rel
2
rel
22
2
2
22
rel
2
rel
2
2
2
2
rel
2
rel
2
2
2
2
rel
2
rel
2
2
2
2
rel
2
2rel
cmcPEcmcPcm
cmPcmcmPcmcPPcP
P
c
PP
c
1
P
P
c
1
P
P
‫ﻞ‬‫ﺣ‬‫اﺧﺮ‬:
cmcPEcmcmE)cm(
c
)cm(E
E
c
EEE
c
EE
c
1
E
E
c
1
E
E
οο
ϑο
οοο
οο
οο
+=⇒+=
+=⇒υ+υ=υ⇒+υ=
=
υ
−⇒
υ
−
=⇒
υ
−
=
+=⇒+υ=⇒+
υ
=
+
υ
=⇒=
υ
−⇒
υ
−
=⇒
υ
−
=
2
relrel c)mm()KE( ο−=
ο−
ν
−
= E)1
c
1
1
()KE(
2
2rel
ο−= EE)KE( relrel
‫اﻟﺴﻜﻮﻧﻴ‬ ‫ﺑﺎﻟﻄﺎﻗﺔ‬ ‫اﻟﻨﺴﺒﻴﺔ‬ ‫اﻟﺤﺮﻛﻴﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ﻋﻼﻗﺔ‬‫ﺔ‬

79. ‫اﻟﻔﺼﻞ‬‫اﻟ‬‫ﻌﺎﺷﺮ‬:‫اﻟ‬‫اﻟﻨﻮوﻳﺔ‬ ‫ﻔﻴﺰﻳﺎء‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-80-
‫ﺸﺤﻨﺔ‬ ‫اﻟ‬ ‫ﺔ‬ ‫اﻟﻤﺘﻌﺎدﻟ‬ ‫ﺎت‬ ‫اﻟﻨﯿﻮﺗﺮوﻧ‬ ‫ﺴﯿﻤﺎت‬ ‫وﺟ‬ ‫ﺸﺤﻨﺔ‬ ‫اﻟ‬ ‫ﺔ‬ ‫اﻟﻤﻮﺟﺒ‬ ‫ﺎت‬ ‫اﻟﺒﺮوﺗﻮﻧ‬ ‫ﺴﯿﻤﺎت‬ ‫ﺟ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﻮاة‬ ‫اﻟﻨ‬ ‫ﻮن‬ ‫ﺗﺘﻜ‬
)‫ﻔﺮ‬‫ﺻ‬ ‫ﺴﺎوي‬ ‫ﺗ‬ ‫ﻮﺗﺮون‬‫اﻟﻨﯿ‬ ‫ﺤﻨﺔ‬‫ﺷ‬.(‫ﻦ‬‫ﻣ‬ ‫ﻮن‬‫ﺗﺘﻜ‬ ‫ﻮاة‬ ‫اﻟﻨ‬ ‫ان‬ ‫ﻲ‬‫ﯾﻌﻨ‬ ‫ﺬا‬‫وھ‬ ‫ﺔ‬ ‫اﻟﻨﻮﯾ‬ ‫او‬ ‫ﺎت‬‫ﺑﺎﻟﻨﯿﻮﻛﻠﯿﻮﻧ‬ ‫ﺎ‬ ‫ﻣﻨﮭﻤ‬ ‫ﻞ‬‫ﻛ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﻖ‬ ‫ﯾﻄﻠ‬
‫اﻟﻨﯿﻮﻛﻠﯿﻮﻧﺎت‬.‫ﻟﻠﺒﺮوﺗﻮن‬ ‫ﯾﺮﻣﺰ‬)H1
1(‫او‬)P(‫او‬)P1
1(‫ﺑﺎﻟﺮﻣﺰ‬ ‫ﻟﻠﻨﯿﻮﺗﺮون‬ ‫وﯾﺮﻣﺰ‬)n1
0(‫او‬)n.(
‫اﻟﺬري‬ ‫اﻟﻌﺪد‬:‫اﻟﻌﻨﺼﺮ‬ ‫رﻣﺰ‬ ‫ﯾﺴﺎر‬ ‫ﻋﺎدة‬ ‫وﯾﻜﺘﺐ‬ ‫اﻟﻨﻮاة‬ ‫ﻓﻲ‬ ‫اﻟﺒﺮوﺗﻮﻧﺎت‬ ‫ﻋﺪد‬ ‫ھﻮ‬)‫ﻮاة‬‫اﻟﻨ‬ ‫رﻣﺰ‬ ‫او‬(‫ﻔﻞ‬‫اﻻﺳ‬ ‫ﻦ‬‫ﻣ‬.‫ﮫ‬‫ﻟ‬ ‫ﺰ‬‫وﯾﺮﻣ‬
‫ﺑﺎﻟﺮﻣﺰ‬)Z.(
‫اﻟﻜﺘﻠﻲ‬ ‫اﻟﻌﺪد‬:‫واﻟﻨ‬ ‫اﻟﺒﺮوﺗﻮﻧﺎت‬ ‫ﻋﺪد‬ ‫ﻣﺠﻤﻮع‬ ‫ھﻮ‬‫ﺼﺮ‬‫اﻟﻌﻨ‬ ‫ﺰ‬‫رﻣ‬ ‫ﺴﺎر‬‫ﯾ‬ ‫ﻋﺎدة‬ ‫وﯾﻜﺘﺐ‬ ‫اﻟﻨﻮاة‬ ‫ﻓﻲ‬ ‫ﯿﻮﺗﺮوﻧﺎت‬)‫ﻮاة‬‫اﻟﻨ‬ ‫ﺰ‬‫رﻣ‬ ‫او‬
)X((‫اﻻﻋﻠﻰ‬ ‫اﻟﻰ‬.‫ﺑﺎﻟﺮﻣﺰ‬ ‫ﻟﮫ‬ ‫وﯾﺮﻣﺰ‬)A.(
•‫و‬‫اﻻﺗﻴﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬ ‫اﻟﻜﺘﻠﺔ‬ ‫ﻋﺪد‬ ‫او‬ ‫اﻟﻜﺘﻠﻲ‬ ‫اﻟﻌﺪد‬ ‫اﻳﺠﺎد‬ ‫ﻳﻤﻜﻦ‬:
‫ﺣﯿﺚ‬:
A:‫ﯾﻜ‬ ‫واﻟﺬي‬ ‫اﻟﻜﺘﻠﺔ‬ ‫ﺑﻌﺪد‬ ‫اﺣﯿﺎﻧﺎ‬ ‫ﯾﺴﻤﻰ‬ ‫واﻟﺬي‬ ‫اﻟﻜﺘﻠﻲ‬ ‫اﻟﻌﺪد‬ ‫ﯾﻤﺜﻞ‬‫اﻟﻨﻮاة‬ ‫رﻣﺰ‬ ‫ﯾﺴﺎر‬ ‫ﻋﺎدة‬ ‫ﺘﺐ‬)X(‫ذﻛﺮﻧﺎ‬ ‫ﻛﻤﺎ‬ ‫اﻻﻋﻠﻰ‬ ‫اﻟﻰ‬
Z:‫اﻟﻨﻮاة‬ ‫رﻣﺰ‬ ‫ﯾﺴﺎر‬ ‫ﯾﻜﺘﺐ‬ ‫واﻟﺬي‬ ‫اﻟﺬري‬ ‫اﻟﻌﺪد‬)X(‫اﻻﺳﻔﻞ‬ ‫ﻣﻦ‬.
N:‫اﻟﻨﯿﻮﺗﺮوﻧﻲ‬ ‫اﻟﻌﺪد‬.
‫اﻟﻨﻴﻮﺗﺮوﻧﻲ‬ ‫اﻟﻌﺪد‬:‫اﻟﻨﻮاة‬ ‫ﻓﻲ‬ ‫اﻟﻨﯿﻮﺗﺮوﻧﺎت‬ ‫ﻋﺪد‬ ‫ھﻮ‬.‫ﺎﻟﺮﻣﺰ‬‫ﺑ‬ ‫ﮫ‬‫ﻟ‬ ‫ﺰ‬‫وﯾﺮﻣ‬)N(‫ﺪد‬‫واﻟﻌ‬ ‫ﻲ‬‫اﻟﻜﺘﻠ‬ ‫ﺪد‬‫اﻟﻌ‬ ‫ﯿﻦ‬‫ﺑ‬ ‫ﺮق‬‫اﻟﻔ‬ ‫ﺴﺎوي‬‫وﯾ‬
‫اﻟﺬري‬.
‫ان‬ ‫أي‬:
‫ﯾﻜﺘﺐ‬ ‫ﻛﯿﻒ‬ ‫ﻻﺣﻆ‬‫اﻟﺬري‬ ‫اﻟﻌﺪد‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬)Z(‫اﻟﻜﺘﻠﺔ‬ ‫وﻋﺪد‬)A(‫اﻟﻨﻮاة‬ ‫رﻣﺰ‬ ‫اﻟﻰ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬)X.(
‫ﻣﺜﺎل‬/‫ﻟﻼﻧﻮﯾﺔ‬ ‫اﻟﻨﯿﻮﺗﺮوﻧﻲ‬ ‫واﻟﻌﺪد‬ ‫اﻟﻜﺘﻠﻲ‬ ‫واﻟﻌﺪد‬ ‫اﻟﺬري‬ ‫اﻟﻌﺪد‬ ‫ﺟﺪ‬:
Fe,mg,Al 56
26
25
12
27
13
‫ج‬/
302656ZAN,56A,26Z:Fe
131225ZAN,25A,12Z:Mg
141327ZAN,27A,13Z:Al
56
26
25
12
27
13
=−=−===
=−=−===
=−=−===
‫ﺣﺴ‬‫ﻟﻠﻨﻮاة‬ ‫اﻟﺘﻘﺮﻳﺒﻴﺔ‬ ‫اﻟﻜﺘﻠﺔ‬ ‫ﺎب‬:
‫ﺎ‬ ‫ورﻣﺰھ‬ ‫ﻮاة‬ ‫ﻟﻠﻨ‬ ‫ﺔ‬ ‫اﻟﺘﻘﺮﯾﺒﯿ‬ ‫ﺔ‬ ‫اﻟﻜﺘﻠ‬ ‫ان‬)
−
m(‫ﺎ‬ ‫ورﻣﺰھ‬ ‫ﺔ‬ ‫اﻟﺬرﯾ‬ ‫ﻞ‬ ‫اﻟﻜﺘ‬ ‫ﺪة‬ ‫وﺣ‬ ‫ﺴﻤﻰ‬ ‫ﺗ‬ ‫ﺪة‬ ‫ﺑﻮﺣ‬ ‫ﺎ‬ ‫ﻣﻘﺎﺳ‬ ‫ﻲ‬ ‫اﻟﻜﺘﻠ‬ ‫ﺪد‬ ‫اﻟﻌ‬ ‫ﺴﮭﺎ‬ ‫ﻧﻔ‬ ‫ﻲ‬ ‫ھ‬
)amu(‫واﺧﺘﺼﺎرا‬)u(‫اﻟﻜﯿﻠﻮﻏﺮام‬ ‫وﺣﺪة‬ ‫ﻣﻦ‬ ‫ﺑﺪﻻ‬)kg(‫ان‬ ‫أي‬:
‫اﻟ‬ ‫ﺗﻘﺎس‬ ‫ان‬ ‫وﯾﻤﻜﻦ‬‫ﺑﻮﺣﺪة‬ ‫اﻟﺘﻘﺮﯾﺒﯿﺔ‬ ‫ﻜﺘﻠﺔ‬)kg(‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫اﻣﺎ‬ ، ‫ﻛﺬﻟﻚ‬)u(‫و‬)kg(‫ﻓﮭﻲ‬:
‫ـﻦ‬‫ـ‬‫ﻣـ‬ ‫اﻟﻨــﻮاة‬ ‫ـﺔ‬‫ـ‬‫ﻛﺘﻠـ‬ ‫ﻟﺘﺤﻮﻳــﻞ‬ ‫ﻟــﺬﻟﻚ‬)kg(‫اﻟــﻰ‬)u(‫ـﻰ‬‫ـ‬‫ﻋﻠـ‬ ‫ﻧﻘــﺴﻢ‬1.66×10-27
‫ـﻲ‬‫ـ‬‫ﻓـ‬ ‫اﻟﻤﻘــﺪار‬ ‫ـﻀﺮب‬‫ـ‬‫ﻧـ‬ ‫وﺑــﺎﻟﻌﻜﺲ‬
1.66×10-27
‫ﻣﻦ‬ ‫ﻟﻠﺘﺤﻮﻳﻞ‬)u(‫اﻟﻰ‬)kg.(
uAm ×=−
ZAN −=
kg1066.1u1amu1 27−
×==
XA
Z
NZA +=

80. ‫اﻟﻔﺼﻞ‬‫اﻟ‬‫ﻌﺎﺷﺮ‬:‫اﻟ‬‫اﻟﻨﻮوﻳﺔ‬ ‫ﻔﻴﺰﻳﺎء‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-81-
‫واﻟﻄﺎﻗﺔ‬ ‫اﻟﻜﺘﻠﺔ‬ ‫ﺗﻜﺎﻓﺆ‬:
♦‫اﻟﻨﻮ‬ ‫اﻟﻔﯿﺰﯾﺎء‬ ‫ﻓﻲ‬‫ﺘﻌﻤﺎل‬‫ﺑﺎﺳ‬ ‫ﻚ‬‫وذﻟ‬ ‫ﺔ‬‫ﻟﻠﻜﺘﻠ‬ ‫ﺔ‬‫اﻟﻤﻜﺎﻓﺌ‬ ‫ﺔ‬‫اﻟﻄﺎﻗ‬ ‫ﺎد‬‫اﯾﺠ‬ ‫ﻦ‬‫ﯾﻤﻜ‬ ‫ﺚ‬‫ﺣﯿ‬ ‫ﺔ‬‫طﺎﻗ‬ ‫ﻦ‬‫ﻣ‬ ‫ﺎ‬‫ﯾﻜﺎﻓﺌﮭ‬ ‫ﺎ‬‫ﺑﻤ‬ ‫اﻟﻜﺘﻠﺔ‬ ‫ﻋﻦ‬ ‫ﯾﻌﺒﺮ‬ ‫وﯾﺔ‬
‫اﻟﻜﺘﻠﺔ‬ ‫ﺗﻜﺎﻓﺆ‬ ‫ﻓﻲ‬ ‫اﻟﻤﻌﺮوﻓﺔ‬ ‫اﯾﻨﺸﺘﺎﯾﻦ‬ ‫ﻋﻼﻗﺔ‬)m(‫اﻟﻄﺎﻗﺔ‬ ‫ﻣﻊ‬)E(‫اﻻﺗﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫وﺣﺴﺐ‬:
‫اﻟـ‬ ‫ھﻲ‬ ‫اﻟﻜﺘﻠﺔ‬ ‫وﺣﺪة‬ ‫ﺗﻜﻮن‬ ‫وﻋﻨﺪﻣﺎ‬)u(‫ھﻲ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫وﺣﺪة‬ ‫ﻓﺎن‬)MeV(‫وان‬)c2
=931MeV/u(‫ﺪة‬‫وﺣ‬ ‫ﻮن‬‫ﺗﻜ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻣﺎ‬ ،
‫ھﻲ‬ ‫اﻟﻜﺘﻠﺔ‬)kg(‫وﺣﺪة‬ ‫ﻓﺎن‬)E(‫وان‬ ‫اﻟﺠﻮل‬ ‫ھﻲ‬)c2
=9×1016
m2
/sec2
. (
‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫اﻣﺎ‬)MeV(‫و‬)J(‫ﻓﮭﻲ‬:
‫ﻣﻦ‬ ‫ﻟﻠﺘﺤﻮﯾﻞ‬ ‫ﻟﺬﻟﻚ‬)MeV(‫اﻟﻰ‬)J(‫ﻲ‬‫ﻓ‬ ‫ﺪار‬‫اﻟﻤﻘ‬ ‫ﻧﻀﺮب‬)1.6×10-13
J(‫ﻦ‬‫ﻣ‬ ‫ﻞ‬‫ﻟﻠﺘﺤﻮﯾ‬ ‫ﺎﻟﻌﻜﺲ‬‫وﺑ‬)J(‫ﻰ‬‫اﻟ‬)MeV(‫ﺴﻢ‬‫ﻧﻘ‬
‫ﻋﻠﻰ‬ ‫اﻟﻤﻘﺪار‬)1.6×10-13
.(
‫اﻟﻨﻮاة‬ ‫ﺷﺤﻨﺔ‬ ‫ﺣﺴﺎب‬:
‫ﻣﺘﻌﺎدﻟﺔ‬ ‫اﻟﻨﯿﻮﺗﺮوﻧﺎت‬ ‫ﻻن‬ ‫ﺑﺮوﺗﻮﻧﺎﺗﮭﺎ‬ ‫ﺷﺤﻨﺔ‬ ‫ﻣﺠﻤﻮع‬ ‫ھﻲ‬ ‫اﻟﻨﻮاة‬ ‫ﺷﺤﻨﺔ‬ ‫ان‬‫اﻟﺸﺤﻨﺔ‬)‫ﻔﺮ‬‫ﺻ‬ ‫ﺴﺎوي‬‫ﺗ‬ ‫ﻮﺗﺮون‬‫اﻟﻨﯿ‬ ‫ﺤﻨﺔ‬‫ﺷ‬(‫ﺚ‬‫وﺣﯿ‬
‫ھﻲ‬ ‫اﻟﻨﻮاة‬ ‫ﺑﺮوﺗﻮﻧﺎت‬ ‫ﻣﻦ‬ ‫ﺑﺮوﺗﻮن‬ ‫ﻛﻞ‬ ‫ﺷﺤﻨﺔ‬ ‫ان‬)+e(‫وان‬)e=1.6×10-19
C(‫ورﻣﺰھﺎ‬ ‫اﻟﻨﻮاة‬ ‫ﺷﺤﻨﺔ‬ ‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬)q(‫ﺗﻌﻄﻰ‬
‫ﯾﻠﻲ‬ ‫ﻛﻤﺎ‬:
‫ﺣﺴﺎب‬‫وﻛﺜﺎﻓﺘﻬﺎ‬ ‫وﺣﺠﻤﻬﺎ‬ ‫اﻟﻨﻮاة‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬:
♦‫اﻟﻨﻮاة‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬ ‫ان‬ ‫وﺟﺪ‬ ‫ﻟﻘﺪ‬)R(‫ﻲ‬‫اﻟﻜﺘﻠ‬ ‫ﺪد‬‫ﻟﻠﻌ‬ ‫ﻲ‬‫اﻟﺘﻜﻌﯿﺒ‬ ‫ﺬر‬‫اﻟﺠ‬ ‫ﻣﻊ‬ ‫طﺮدﯾﺎ‬ ‫ﺗﻐﯿﺮا‬ ‫ﯾﺘﻐﯿﺮ‬)A(‫ﺼﻒ‬‫ﻧ‬ ‫ﺴﺎب‬‫ﺣ‬ ‫ﻦ‬‫وﯾﻤﻜ‬
‫اﻻﺗﯿﺔ‬ ‫ﻟﻠﻌﻼﻗﺔ‬ ‫وﻓﻘﺎ‬ ‫اﻟﻘﻄﺮ‬:
‫ﺣﯿﺚ‬:
)ο
r(‫وﯾﺴﺎوي‬ ‫اﻟﻘﻄﺮ‬ ‫ﻧﺼﻒ‬ ‫ﺛﺎﺑﺖ‬ ‫ﯾﺴﻤﻰ‬ ‫ﺛﺎﺑﺖ‬ ‫ﻣﻘﺪار‬ ‫ھﻮ‬)1.2×10-15
m(‫او‬)1.2F(‫ﺮ‬‫اﻟﻘﻄ‬ ‫ﺼﻒ‬‫ﻧ‬ ‫ﺛﺎﺑﺖ‬ ‫ان‬ ‫أي‬)rº(‫ﺎ‬‫اﻣ‬
‫اﻟﻔﯿﺮﻣﻲ‬ ‫او‬ ‫اﻟﻔﯿﻤﺘﻮﻣﺘﺮ‬ ‫ﺗﺴﻤﻰ‬ ‫اﻟﻤﺘﺮ‬ ‫ﻏﯿﺮ‬ ‫اﺧﺮى‬ ‫ﺑﻮﺣﺪة‬ ‫ﯾﻘﺎس‬ ‫او‬ ‫اﻟﻤﺘﺮ‬ ‫ﺑﻮﺣﺪة‬ ‫ﯾﻘﺎس‬ ‫ان‬)Fermi(‫ﺰه‬‫ورﻣ‬)F(‫ﺔ‬‫اﻟﻌﻼﻗ‬ ‫وان‬
‫ﺑﯿﻦ‬)m(‫و‬)F(‫ھﻲ‬:
‫ﻣﻦ‬ ‫ﻟﻠﺘﺤﻮﻳﻞ‬ ‫ﻟﺬﻟﻚ‬)F(‫اﻟﻰ‬)m(‫ﻓﻲ‬ ‫ﻧﻀﺮب‬10-15
‫وﻟﻠﺘﺤﻮﻳﻞ‬‫ﻣﻦ‬)m(‫اﻟﻰ‬)F(‫ﻋﻠﻰ‬ ‫ﻧﻘﺴﻢ‬10-15
.
•‫ﻗﻄﺮه‬ ‫ﻧﺼﻒ‬ ‫ﻛﺮوي‬ ‫ھﻮ‬ ‫اﻟﻨﻮاة‬ ‫ﺷﻜﻞ‬ ‫ان‬ ‫اﻋﺘﺒﺎر‬ ‫وﻋﻠﻰ‬)R(‫اﻟﻨﻮاة‬ ‫ﺣﺠﻢ‬ ‫اﯾﺠﺎد‬ ‫اﻣﻜﻦ‬ ‫ﻟﺬﻟﻚ‬)V(‫اﻟﻌﻼﻗﺎت‬ ‫وﻓﻘﺎ‬‫اﻟﺘﺎﻟﯿﺔ‬:
m10F1 15−
=
J106.1MeV1 13−
×=
Ar
3
4
VorR
3
4
V 33
οπ=π=
33
1
ArRorArR οο ==
Zeq =
2
mcE =

81. ‫اﻟﻔﺼﻞ‬‫اﻟ‬‫ﻌﺎﺷﺮ‬:‫اﻟ‬‫اﻟﻨﻮوﻳﺔ‬ ‫ﻔﻴﺰﻳﺎء‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-82-
•‫ا‬ ‫ﻛﺜﺎﻓﺔ‬ ‫ﻻﯾﺠﺎد‬ ‫اﻣﺎ‬‫اﻟﺘﻘﺮﯾﺒﯿﺔ‬ ‫ﻟﻨﻮاة‬)ρ(‫اﻻﺗﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻓﻨﻄﺒﻖ‬:
‫اﻟﺮﺑﻂ‬ ‫ﻃﺎﻗﺔ‬)‫اﻻرﺗﺒﺎط‬(‫اﻟﻨﻮوﻳﺔ‬)bE:(
‫ﻣﻌﯿﻨﺔ‬ ‫ﻧﻮاة‬ ‫ﻟﺘﺸﻜﯿﻞ‬ ‫واﻟﻨﯿﻮﺗﺮوﻧﺎت‬ ‫اﻟﺒﺮوﺗﻮﻧﺎت‬ ‫ﻣﻦ‬ ‫ﻣﻨﺎﺳﺒﺔ‬ ‫اﻋﺪاد‬ ‫ﺟﻤﻊ‬ ‫ﻋﻨﺪ‬ ‫اﻟﻤﺘﺤﺮرة‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ھﻲ‬)‫اﻟﻼزﻣﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫ھﻲ‬ ‫او‬
‫اﻟﻰ‬ ‫اﻟﻨﻮاة‬ ‫ﻟﺘﻔﻜﯿﻚ‬‫واﻟﻨﯿﻮﺗﺮوﻧﺎت‬ ‫اﻟﺒﺮوﺗﻮﻧﺎت‬ ‫ﻣﻦ‬ ‫ﻣﻜﻮﻧﺎﺗﮭﺎ‬.(
‫اﻧﺘﺒﻪ‬:
♦‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫واﻟﻨﯿﻮﺗﺮوﻧﺎت‬ ‫اﻟﺒﺮوﺗﻮﻧﺎت‬ ‫ﻣﻦ‬ ‫ﻣﻜﻮﻧﺎﺗﮭﺎ‬ ‫ﻛﺘﻞ‬ ‫ﻣﺠﻤﻮع‬ ‫ﺗﺴﺎوي‬ ‫ﻻ‬ ‫اﻟﻨﻮاة‬ ‫ﻛﺘﻠﺔ‬ ‫ان‬‫ﻞ‬‫اﻟﻜﺘ‬ ‫ﺬه‬‫ھ‬‫ﻲ‬‫ﻓﮭ‬ ، ‫ﺼﻠﺔ‬‫ﻣﻨﻔ‬
‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫واﻟﻨﯿﻮﺗﺮوﻧﺎت‬ ‫اﻟﺒﺮوﺗﻮﻧﺎت‬ ‫ﻣﻦ‬ ‫ﻣﻜﻮﻧﺎﺗﮭﺎ‬ ‫ﻛﺘﻞ‬ ‫ﻣﺠﻤﻮع‬ ‫ﻣﻦ‬ ‫اﻗﻞ‬ ‫داﺋﻤﺎ‬‫ﻣﻨﻔﺼﻠﺔ‬.
♦‫ﺑﺎﻟﻜﺘﻠﺔ‬ ‫اﻟﻔﺮق‬ ‫ان‬)m∆(‫ﺔ‬‫اﻟﻨﻮوﯾ‬ ‫ﺮﺑﻂ‬‫اﻟ‬ ‫ﺔ‬‫طﺎﻗ‬ ‫ﺎﻓﺊ‬‫ﯾﻜ‬ ‫اﻧﮫ‬ ‫وﺟﺪ‬ ‫اﻟﻜﺘﻠﻲ‬ ‫ﺑﺎﻟﻨﻘﺺ‬ ‫ﻋﺎدة‬ ‫ﯾﺴﻤﻰ‬ ‫واﻟﺬي‬)Eb(‫ﺔ‬‫ﻋﻼﻗ‬ ‫ﺴﺐ‬‫ﺣ‬
‫ﺑﺘﻜﺎﻓﺆ‬ ‫واﻟﺨﺎﺻﺔ‬ ‫اﻧﺸﺘﺎﯾﻦ‬)‫اﻟﻜﺘﻠﺔ‬–‫اﻟﻄﺎﻗﺔ‬(‫ان‬ ‫أي‬:
‫ﺔ‬ ‫اﻟﻨﻮوﯾ‬ ‫ﺮﺑﻂ‬ ‫اﻟ‬ ‫ﺔ‬ ‫طﺎﻗ‬ ‫ﺪة‬ ‫وﺣ‬)Eb(‫ﻲ‬ ‫ھ‬)MeV(‫ﻲ‬ ‫اﻟﻜﺘﻠ‬ ‫ﻨﻘﺺ‬ ‫اﻟ‬ ‫ﻮن‬ ‫ﯾﻜ‬ ‫ﺪﻣﺎ‬ ‫ﻋﻨ‬)m∆(‫ﺪة‬ ‫ﺑﻮﺣ‬)u(
‫و‬)
u
MeV
931c2
=.(
‫اﻟﻨﻮوﯾ‬ ‫اﻟﺮﺑﻂ‬ ‫طﺎﻗﺔ‬ ‫ﺗﻘﺎس‬ ‫ان‬ ‫ﯾﻤﻜﻦ‬ ‫ﻛﺬﻟﻚ‬‫ﺔ‬)Eb(‫ﺑﺎﻟﺠﻮل‬)J. (
♦‫اﻟﻨﻮى‬ ‫ﻛﺘﻞ‬ ‫اﺳﺘﻌﻤﺎل‬ ‫ﻣﻦ‬ ‫ﺑﺪﻻ‬ ‫اﻟﺬرات‬ ‫ﻛﺘﻞ‬ ‫اﺳﺘﻌﻤﺎل‬ ‫ﻣﻨﺎﺳﺒﺎ‬ ‫اﻛﺜﺮ‬ ‫ﯾﻜﻮن‬ ‫ﻓﺎﻧﮫ‬ ‫اﻟﻌﻤﻠﯿﺔ‬ ‫اﻟﻨﺎﺣﯿﺔ‬ ‫ﻣﻦ‬‫ﻲ‬‫اﻟﻜﺘﻠ‬ ‫ﻨﻘﺺ‬‫اﻟ‬ ‫ﻓﺎن‬ ‫ﻟﺬﻟﻚ‬
)m∆(‫اﻻﺗﯿﺔ‬ ‫ﺑﺎﻟﻌﻼﻗﺔ‬ ‫اﻟﺤﺎﻟﺔ‬ ‫ھﺬه‬ ‫ﻓﻲ‬ ‫ﯾﻌﻄﻰ‬:
‫ﺣﯿﺚ‬:
Z:‫اﻟﺬري‬ ‫اﻟﻌﺪد‬.
MH:‫اﻟﮭﯿﺪروﺟﯿﻦ‬ ‫ذرة‬ ‫ﻛﺘﻠﺔ‬.
N:‫اﻟﻨﯿﻮﺗﺮوﻧﻲ‬ ‫اﻟﻌﺪد‬)‫اﻟﻨﯿﻮﺗﺮوﻧﺎت‬ ‫ﻋﺪد‬ ‫او‬.(
mn:‫اﻟﻨﯿﻮﺗﺮون‬ ‫ﻛﺘﻠﺔ‬.
M:‫اﻟﻤﻌﻨﯿﺔ‬ ‫اﻟﺬرة‬ ‫ﻛﺘﻠﺔ‬.
‫اﻟﻜﺘﻠﻲ‬ ‫اﻟﻨﻘﺺ‬ ‫وﺑﺘﻌﻮﯾﺾ‬)m∆(‫اﻟﻨﻮوﯾ‬ ‫اﻟﺮﺑﻂ‬ ‫طﺎﻗﺔ‬ ‫ﻓﻲ‬‫ﺔ‬‫ﻟﻠﻨﻮاة‬)Eb(‫اﻟﻨﻮوﯾ‬ ‫اﻟﺮﺑﻂ‬ ‫طﺎﻗﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫ﺗﺼﺒﺢ‬‫ﺔ‬‫اﻻﺗﻲ‬ ‫ﺑﺎﻟﺸﻜﻞ‬:
‫ﺪة‬ ‫ﺑﻮﺣ‬ ‫ﺎس‬ ‫ﺗﻘ‬ ‫ﺔ‬ ‫اﻟﺬرﯾ‬ ‫ﻞ‬ ‫اﻟﻜﺘ‬ ‫ان‬ ‫ﺎ‬ ‫وﺑﻤ‬)u(‫اﻟﻨﻮوﯾ‬ ‫ﺮﺑﻂ‬ ‫اﻟ‬ ‫ﺔ‬ ‫طﺎﻗ‬ ‫ﺎن‬ ‫ﻓ‬‫ﺔ‬)Eb(‫ﺪة‬ ‫ﺑﻮﺣ‬ ‫ﺎس‬ ‫ﺗﻘ‬)MeV(‫ان‬ ‫اذ‬
)
u
MeV
931c2
=.(
2
nHb c)MNmZM(E −+=
MNmZMm nH −+=∆
2
b cmE ∆=
V
m−
=ρ

82. ‫اﻟﻔﺼﻞ‬‫اﻟ‬‫ﻌﺎﺷﺮ‬:‫اﻟ‬‫اﻟﻨﻮوﻳﺔ‬ ‫ﻔﻴﺰﻳﺎء‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-83-
‫ﻣﻌﺪل‬)‫ﻣﺘﻮﺳﻂ‬(‫اﻟﺮﺑ‬ ‫ﻃﺎﻗﺔ‬‫ﻧﻴﻮﻛﻠـﻮن‬ ‫ﻟﻜﻞ‬ ‫اﻟﻨﻮوﻳﺔ‬ ‫ﻂ‬)‫ﻟﻠﻨﻴﻮﻛﻠ‬ ‫او‬‫ﻴـ‬‫ﻮن‬)(−
b
E: (‫ﺔ‬‫اﻟﻨﻮوﯾ‬ ‫ﺮﺑﻂ‬‫اﻟ‬ ‫ﺔ‬‫طﺎﻗ‬ ‫ﺴﻤﺔ‬‫ﻗ‬ ‫ﻞ‬‫ﺣﺎﺻ‬ ‫ﻮ‬‫ھ‬
)Eb(‫اﻟﻜﺘﻠﻲ‬ ‫اﻟﻌﺪد‬ ‫ﻋﻠﻰ‬)A.(
‫ان‬ ‫أي‬:
‫وﺣﺪة‬)−
b
E(‫ھﻲ‬)MeV/nucleon(‫او‬)MeV.(
‫اﻻﺷﻌﺎﻋﻲ‬ ‫اﻻﻧﺤﻼل‬:
‫اﻧﻮاع‬ ‫ﺛﻼﺛﺔ‬ ‫ھﻨﺎﻟﻚ‬‫ھﻲ‬ ‫اﻻﺷﻌﺎﻋﻲ‬ ‫ﻟﻼﻧﺤﻼل‬ ‫رﺋﯿﺴﯿﺔ‬:
1-‫اﻟﻔﺎ‬ ‫اﻧﺤﻼل‬2-‫ﺑﯿﺘﺎ‬ ‫اﻧﺤﻼل‬3-‫ﻛﺎﻣﺎ‬ ‫اﻧﺤﻼل‬َ.
•‫ﻼل‬‫اﻻﻧﺤ‬ ‫ﺪ‬‫ﺑﻌ‬ ‫ﺔ‬‫اﻟﻨﺎﺗﺠ‬ ‫ﻮاة‬‫اﻟﻨ‬ ‫ﺎ‬‫اﻣ‬ ‫اﻻم‬ ‫ﻮاة‬‫اﻟﻨ‬ ‫ﻣﺼﻄﻠﺢ‬ ‫اﻻﻧﺤﻼل‬ ‫ﻗﺒﻞ‬ ‫اﻻﺻﻠﯿﺔ‬ ‫اﻟﻨﻮاة‬ ‫ﻋﻠﻰ‬ ‫ﯾﻄﻠﻖ‬ ‫اﻻﻧﺤﻼل‬ ‫اﻧﻮاع‬ ‫ﻛﻞ‬ ‫ﻓﻲ‬
‫اﻟﺒﻨﺖ‬ ‫او‬ ‫اﻟﻮﻟﯿﺪة‬ ‫اﻟﻨﻮاة‬ ‫ﻣﺼﻄﻠﺢ‬ ‫ﻋﻠﯿﮭﺎ‬ ‫ﻓﯿﻄﻠﻖ‬.
‫اﻟﻔﺎ‬ ‫اﻧﺤﻼل‬)α(:
‫ﺎ‬ ‫اﻟﻔ‬ ‫ﺴﯿﻤﺔ‬‫ﺟ‬:‫ﺎﻟﺮﻣﺰ‬‫ﺑ‬ ‫ﻞ‬ ‫وﺗﻤﺜ‬ ‫ﻮﺗﺮوﻧﯿﻦ‬‫وﻧﯿ‬ ‫ﻮﻧﯿﻦ‬ ‫ﺑﺮوﺗ‬ ‫ﻦ‬‫ﻣ‬ ‫ﻮن‬ ‫وﺗﺘﻜ‬ ‫ﻮم‬‫اﻟﮭﯿﻠﯿ‬ ‫ذرة‬ ‫ﻮاة‬ ‫ﻧ‬ ‫ﻲ‬‫ھ‬)He4
2
(‫او‬)α(‫ذات‬ ‫ﻲ‬‫وھ‬
‫ﺗﺴﺎوي‬ ‫ﻣﻮﺟﺒﺔ‬ ‫ﺷﺤﻨﺔ‬‫اﻟﺒﺮوﺗﻮن‬ ‫ﺷﺤﻨﺔ‬ ‫ﺿﻌﻒ‬)+2e.(
‫اﻟﻨﻮوﻳﺔ‬ ‫اﻟﻤﻌﺎدﻟﺔ‬‫اﻟﻌﺎﻣﺔ‬‫اﻟﻔﺎ‬ ‫اﻧﺤﻼل‬ ‫ﺑﻮﺳﺎﻃﺔ‬ ‫ﺗﻠﻘﺎﺋﻴﺎ‬ ‫ﻧﻮاة‬ ‫ﻻﻧﺤﻼل‬‫ﻫﻲ‬:
•‫ھﻲ‬ ‫اﻻم‬ ‫اﻟﻨﻮاة‬ ‫ﻛﺘﻠﺔ‬ ‫ان‬ ‫ﻧﻔﺮض‬ ‫اﻟﻔﺎ‬ ‫اﻧﺤﻼل‬ ‫ﺑﻮﺳﺎطﺔ‬ ‫ﺗﻨﺤﻞ‬ ‫ﻟﻨﻮاة‬ ‫اﻻﻧﺤﻼل‬ ‫طﺎﻗﺔ‬ ‫ﻻﯾﺠﺎد‬)Mp) (‫ﺪاﺋﯿﺎ‬‫اﺑﺘ‬ ‫ﺎﻛﻨﺔ‬‫ﺳ‬ ‫ﺎدة‬‫ﻋ‬(
‫ﻲ‬‫ھ‬ ‫ﺪة‬‫اﻟﻮﻟﯿ‬ ‫ﻮاة‬‫اﻟﻨ‬ ‫وﻛﺘﻠﺔ‬)Md(‫ﻲ‬‫ھ‬ ‫ﺎ‬‫اﻟﻔ‬ ‫ﺴﯿﻤﺔ‬‫ﺟ‬ ‫ﺔ‬‫وﻛﺘﻠ‬)Mα(‫ﺎ‬‫اﻟﻔ‬ ‫ﻼل‬‫اﻧﺤ‬ ‫ﺔ‬‫طﺎﻗ‬ ‫ﺎن‬‫ﻓ‬)Qα(‫ﺔ‬‫اﻟﻌﻼﻗ‬ ‫ﻖ‬‫وﻓ‬ ‫ﻰ‬‫ﺗﻌﻄ‬
‫اﻟﺘﺎﻟﯿﺔ‬:
‫وﻋﻨﺪﻣﺎ‬‫ﺑﻮﺣﺪة‬ ‫اﻟﺬرﯾﺔ‬ ‫اﻟﻜﺘﻞ‬ ‫ﺗﻘﺎس‬)u(‫ان‬ ‫اذا‬)
u
MeV
931c2
=(‫وﺣﺪة‬ ‫ﻓﺎن‬)Qα(‫ھﻲ‬)MeV.(
‫ﻗﯿﻤﺔ‬ ‫ﺗﻜﻮن‬ ‫ان‬ ‫اﻟﺘﻠﻘﺎﺋﻲ‬ ‫اﻻﻧﺤﻼل‬ ‫ﺷﺮط‬ ‫وان‬)Qα(‫اﻟﺼﻔﺮ‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫أي‬ ‫ﻣﻮﺟﺒﺔ‬.
‫َﺎﻣﺎ‬‫ﻛ‬ ‫اﻧﺤﻼل‬)γ: (
‫ﻛﺎﻣﺎ‬ ‫اﺷﻌﺔ‬َ:‫ﻛﮭﺮوﻣﻐﻨﺎطﯿﺴﯿﺔ‬ ‫اﺷﻌﺔ‬ ‫ھﻲ‬)‫ﻓﻮﺗﻮﻧﺎت‬(‫ا‬ ‫ﻛﺘﻠﺘﮭﺎ‬ ، ‫ﻋﺎل‬ ‫ﺗﺮدد‬ ‫او‬ ‫ﻋﺎﻟﯿﺔ‬ ‫طﺎﻗﺔ‬ ‫ذات‬‫ﺴﺎوي‬‫ﺗ‬ ‫ﺤﻨﺘﮭﺎ‬‫وﺷ‬ ‫ﻟﺴﻜﻮﻧﯿﺔ‬
‫ﺑﺎﻟﺮﻣﺰ‬ ‫ﻟﮭﺎ‬ ‫وﯾﺮﻣﺰ‬ ‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬)γ(‫او‬)γ0
0(‫ﺻﻔﺮ‬ ‫ﯾﺴﺎوي‬ ‫ﻟﮭﺎ‬ ‫اﻟﻜﺘﻠﻲ‬ ‫واﻟﻌﺪد‬ ‫اﻟﺬري‬ ‫اﻟﻌﺪد‬ ‫ان‬ ‫اذ‬ ،.
•‫اﻟﻌﺎﻣﺔ‬ ‫اﻟﻤﻌﺎدﻟﺔ‬‫ﻟﻨﻮاة‬‫ﻛﺎﻣﺎ‬ ‫اﻧﺤﻼل‬ ‫ﺗﻌﺎﻧﻲ‬َ‫ھﻲ‬:
)‫اﻟﻨﺠﻤﺔ‬ ‫اﺷﺎرة‬(*)‫اﺛﺎرة‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬ ‫ھﻲ‬ ‫اﻟﻨﻮاة‬ ‫ان‬ ‫ﺗﺒﯿﻦ‬‫ﺗﮭﯿﺞ‬ ‫او‬.(
HeyX 4
2
4A
2Z
A
z +→ −
−
)‫اﻟﻔﺎ‬ ‫ﺟﺴﯿﻤﺔ‬) (‫اﻟﻮﻟﯿﺪة‬ ‫اﻟﻨﻮاة‬) (‫اﻻم‬ ‫اﻟﻨﻮاة‬(
γ+→ 0
0
A
Z
*A
Z XX
)‫ﻛﺎﻣﺎ‬ ‫اﺷﻌﺔ‬َ) (‫اﻟﻮﻟﯿﺪة‬ ‫اﻟﻨﻮاة‬) (‫اﻻم‬ ‫اﻟﻨﻮاة‬(
‫اﻟﻤﺘﮭﯿﺠﺔ‬
A
E
E b
b =−
2
dp c]MMM[Q αα −−=

83. ‫اﻟﻔﺼﻞ‬‫اﻟ‬‫ﻌﺎﺷﺮ‬:‫اﻟ‬‫اﻟﻨﻮوﻳﺔ‬ ‫ﻔﻴﺰﻳﺎء‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-84-
•‫اﻟﺘ‬ ‫ﯾﻤﻜﻦ‬‫ﻛﺎﻣﺎ‬ ‫اﺷﻌﺔ‬ ‫طﺎﻗﺔ‬ ‫ﻋﻼﻗﺔ‬ ‫ﻋﻦ‬ ‫ﻌﺒﯿﺮ‬َ)‫اﻟﻔﻮﺗﻮن‬ ‫طﺎﻗﺔ‬()E(‫ﺑﺎﻟﺘﺮدد‬)f(‫اﻟﻤﻮﺟﻲ‬ ‫ﺑﺎﻟﻄﻮل‬ ‫او‬)λ(‫ﯾﺄﺗﻲ‬ ‫ﻛﻤﺎ‬:
‫ﺣﯿﺚ‬:
h:‫ﺑﻼﻧﻚ‬ ‫ﺛﺎﺑﺖ‬)h=6.63×10-34
J.s.(
c:‫اﻟﻔﺮاغ‬ ‫ﻓﻲ‬ ‫اﻟﻀﻮء‬ ‫ﺳﺮﻋﺔ‬)c=3×108
m/s.(
λ:‫اﻟﻔﻮﺗﻮن‬ ‫ﻣﻮﺟﺔ‬ ‫طﻮل‬.
‫اﻟﺘﻔﺎﻋﻞ‬ ‫ﻃﺎﻗﺔ‬‫اﻟﻨﻮوي‬:
‫اﻟﮭﺪف‬ ‫اﻟﻨﻮاة‬ ‫ﻓﯿﮫ‬ ‫ﺗﻘﺬف‬ ‫ﻧﻮوﯾﺎ‬ ‫ﺗﻔﺎﻋﻼ‬ ‫ان‬ ‫اﻓﺘﺮﺿﻨﺎ‬ ‫اذا‬)X) (‫اﺑﺘﺪاﺋﯿﺎ‬ ‫ﺳﺎﻛﻨﺔ‬ ‫ﻋﺎدة‬(‫ﻛﺘﻠﺘﮭﺎ‬ ‫واﻟﺘﻲ‬)Mx(‫ﺴﺎﻗﻂ‬‫اﻟ‬ ‫ﺴﯿﻢ‬‫ﺑﺎﻟﺠ‬
)‫اﻟﻤﻘﺬوف‬) (a(‫ﻛﺘﻠﺘﮫ‬ ‫واﻟﺬي‬)Ma(‫ﻧﻮاة‬ ‫ﻟﯿﻨﺘﺞ‬)Y(‫ﻛﺘﻠﺘﮭﺎ‬ ‫واﻟﺘﻲ‬)My(‫واﻟﺠﺴﯿﻢ‬)b(‫ﻛﺘﻠﺘﮫ‬ ‫اﻟﺬي‬)Mb.(
‫ﺑﺎﻟﻤﻌﺎدﻟﺔ‬ ‫اﻟﻨﻮوي‬ ‫اﻟﺘﻔﺎﻋﻞ‬ ‫ھﺬا‬ ‫ﻋﻦ‬ ‫اﻟﺘﻌﺒﯿﺮ‬ ‫ﯾﻤﻜﻦ‬‫اﻟﻨﻮوﯾﺔ‬‫اﻵﺗﯿﺔ‬:
‫اﻟﻨﻮوي‬ ‫اﻟﺘﻔﺎﻋﻞ‬ ‫ﻃﺎﻗﺔ‬ ‫ﻗﻴﻤﺔ‬ ‫ان‬)Q(‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬ ‫اﻳﺠﺎدﻫﺎ‬ ‫ﻳﻤﻜﻦ‬‫اﻵﺗﻴﺔ‬:
or
‫ﺪة‬ ‫ﺑﻮﺣ‬ ‫ﺔ‬ ‫اﻟﺬرﯾ‬ ‫ﻞ‬ ‫اﻟﻜﺘ‬ ‫ﺎس‬ ‫ﺗﻘ‬ ‫ﺪﻣﺎ‬ ‫وﻋﻨ‬)u(‫ﺎن‬ ‫ﻓ‬)
u
MeV
931c2
=(‫طﺎﻗ‬ ‫ﺪة‬ ‫وﺣ‬ ‫ﻮن‬ ‫وﺗﻜ‬‫ﻮوي‬ ‫اﻟﻨ‬ ‫ﻞ‬ ‫اﻟﺘﻔﺎﻋ‬ ‫ﺔ‬)Q(‫ﻲ‬ ‫ھ‬
)MeV.(
‫ﻛﺎﻧﺖ‬ ‫اذا‬ ‫ﻟﻠﻄﺎﻗﺔ‬ ‫ﻣﺤﺮر‬ ‫اﻟﻨﻮوي‬ ‫اﻟﺘﻔﺎﻋﻞ‬ ‫ﯾﺴﻤﻰ‬‫ﺔ‬‫ﻗﯿﻤ‬)Q(‫ﺔ‬‫ﻣﻮﺟﺒ‬)Q >0(‫ﺖ‬‫ﻛﺎﻧ‬ ‫اذا‬ ‫ﺔ‬‫ﻟﻠﻄﺎﻗ‬ ‫ﺎص‬‫ﻣ‬ ‫ﺴﻤﻰ‬‫وﯾ‬‫ﺔ‬‫ﻗﯿﻤ‬)Q(
‫ﺳﺎﻟﺒﺔ‬)Q <0(.
[ ] 2
byba cMMMMQ −−+=
[ ] 2
byba c)MM()MM(Q +−+=
λ
==
ch
EorhfE
bYXa +→+
)‫اﻟﻨﺎﺗﺞ‬ ‫اﻟﺠﺴﯿﻢ‬) (‫اﻟﻨﺎﺗﺠﺔ‬ ‫اﻟﻨﻮاة‬) (‫اﻟﮭﺪف‬ ‫اﻟﻨﻮاة‬) (‫اﻟﺴﺎﻗﻂ‬ ‫او‬ ‫اﻟﻤﻘﺬوف‬ ‫اﻟﺠﺴﯿﻢ‬(

84. ‫اﻟﻔﺼﻞ‬‫اﻟ‬‫ﻌﺎﺷﺮ‬:‫اﻟ‬‫اﻟﻨﻮوﻳﺔ‬ ‫ﻔﻴﺰﻳﺎء‬‫اﻟﻤﺪرس‬ ‫اﻋﺪاد‬:‫ﺗﻮﻣﺎن‬ ‫ﻣﺤﻲ‬ ‫ﺳﻌﻴﺪ‬
-85-
‫ﻗﻮاﻧﻴ‬‫ﻦ‬‫اﻟﻌﺎﺷﺮ‬ ‫اﻟﻔﺼﻞ‬
m10F1,J106.1MeV1,kg1066.1u1
‫اﻟﺘﺤﻮﯾﻼت‬:
c)MMMM(Q,c)MMM(Q
fc,
ch
EorhfE
A
E
'E,MNmZMm,c)MNmZM(EorcmE
V
'm
,Ar
3
4
VorR
3
4
V
ArRorArR,Zeq,mcE,Au'm,NZA,X
151327
2
byxa
2
dp
b
bnH
2
nHb
2
b
33
3
1
32A
Z
−−−
αα
ο
οο
=×=×=
−−+=−−=
λ=
λ
==
=−+=∆−+=∆=
=ρπ=π=
=====+=