1.    SchoolDD.com
17
N S
www.schoolDD.com

2. 17
17.1 ˂ ˂
F 16 ˂ F F F F F
I
I
B B I
I
F (Michael Faraday) F F F F F F
˂ F ˂ F ˂ F
˂ F ˂ F F ˂
17.1.1 ˂ F F F
ሬറ
B
I
ሬറ
B
e Q
I I
P ሬറ
v
ሬറ
B
ሬറ
v
F F F F F ˂ F
F F v
ሬറ F ሬറ
B F
F F F F F
P Q( ) F ˂ F Q P
˂ Q P F F ˂ F P Q F F
F F F ˈ F F ˂ ˂
F ˂
F ˆ F www.schoolDD.com 1

3. 17.1.2 ˂ F F F
F F F F
ሬറ1 F ሬറ2
B
F B
I
N
N
B2 > B1
. F F F F F ∆B = B2 - B1
ሬറ ሬറ ሬറ
˂ I
I
N
N
B2 < B1
. F F F F ∆B = ሬറ2 - ሬറ1
ሬറ B B
˂ I
F F F ˂
F ˂ F
F FF ˂ F F F F
F F
ሬറ
∆B
∆ ሬറ = ሬറ2 - ሬറ1
B B B
I ሬറ
BI
ሬറ
B2
ሬറ1
B
ሬറ ሬറ ሬറ
∆ B = B2 - B1
I ሬറI
B
ሬറ
B1
ሬറ
B2
ሬറ
∆B
F ˆ F www.schoolDD.com 2

4. F 1
˂
. ሬറ
B . ሬറ
B
v v
. . . .
N N S S
. . . .
N N S S
17.1.3 ˂ F F
y
Q R
N v I
B S
I B
v
P S
x
F PQRS F F
xy F v F B F ˂
˂ F F PQ RS ˂ F F PS
QR F ˂ ˂ F
F
F ˆ F www.schoolDD.com 3

5. 17.1.4 ˂ F
F 16 F ˂ I1 F F
F B F F .
N I1 F B S N v I S
B B 2
F I1 I2 B
v
. F ˂ . ˂
˂ F ˂
I2 . F ˂ F F I1 ˂
F F ˂ ˂ F ˂
F (Back emf)
˂ F F
1. F v=0 F F ˂ I2 = 0 ˂
F F F I1- I2 = I1 F ˂ ˂ F
2. F ˂ I2 F ˂ ˂ F I1 F
˂ F F ˈ I = I1- I2 F F (v ) F I2
˂ F F F (Imin)
3. F F ˀ ˂ I2 F
F F ˂ F F ˂ F F ˈ
F F F F ˈ F F
F ˈ F F ˂
F 2
F F ˂ 12 F F ˂ 10 F
˂ F F8 F F F F
F ˆ F www.schoolDD.com 4

6. I1
˂ F F I = I1 I2 I2
୚ ୚
= ୖభ - ୖమ 12 V M
ଵଶ ଵ଴
I
8= ୖ-ୖ
ଶ
8=ୖ
ଵ
R=ସ
‫ ׵‬R = 0.25 Ω Ans
17.2 ˂
˂ ˈ F ˂ F ˈ
˂ F ˂ ˂ F F 2
˂ ˂
17.2.1 ˂
˂ I
N v I S
B 2
I2 B 0 t
v ߨ/4 ߨ/2 3ߨ/4 ߨ
F
F
F F F F F
˂ ˂ ˈ ˂ F
˂ F F F
F F
F F ˂ F F
˂ F F ˈ F
F F F ˂ F
ˈ F F F F ˂
F I t ˂ F ˂ F ˂
(Direct Current D.C )
F ˆ F www.schoolDD.com 5

7. 17.2.2 ˂
˂ I
N v I S
B 2
I2 B 0 t
v ߨ/4 ߨ/2 3ߨ/4 ߨ
F
F ˂ F F ˈ
2 F ˂ ˂ F
F ˂ F ˂ F ˂
(Alternating Current A.C. )
F F F ˂ F ˂ F F
F F F F
˂ I F FV
0 t 0 t
T/2 T 3T/2 2T T/2 T 3T/2 2T
1 1
T 1 F f ˈ F
1 ˂ F 50 F (
50 Hz) F 50 1 F F ˈ 220 F
N S
F ˆ F www.schoolDD.com 6

8. ˈ ˂ F F F F F F
˂ F F FF
17.2.3 ˂ 3
2 1
N S
3
ˈ ˂ F ˂ F
3 120° F F F F F
F F F ˂ ˂
F F 120° F FF F F
F F F F F F F
F
F FV
t 1
t 2
t 3
F ˆ F www.schoolDD.com 7

9. F ˂
C B
220 V
2 1
F F
N S F3
3
D A
E F 220 V
3 220 V
˂
( F BDF F F )
˂ 3 F 6 F F
F F F F F F F ˂ ˈ F F
(N) F F 3 F ˈ F ˂ F F ˂ ( L)
F ˂ ˂ F ˂ 3 4 (L 3 +N1
) ˂ F F ˈ ˂ F F ˂
3 ˂ F F ˂ F F F F F
F F ˈ F ˂ F F F ˂ 3 F
3 ˂ 3 F F F ˂
F F ˂ 3 F ˂ F ˈ 3 F F FF
F F ˈ F F F ˂
˂ F ˂ ˂ F
˂ ˈ F ˈ ˂ F ˂
F F F F F F F
F F ˈ F ˂ F
˂ F F F F F ˂
F
˂ F ˂
˂ F ˂ F
F F F F
F ˆ F www.schoolDD.com 8

10. W = QV
W = ItV (I = Q/t)
W = I2Rt
୛
P= ୲
ItV
P= ୲
P = IV
F 3
˂ F F ˂ F 110 F F
F F ˂ F 100 F 0.20 F 10 F F F
. 220 F . 220,000 F
F P = 110x103 W , R = 0.20 Ω , t = 10 s
. V= 220 V , W = ?
W = I2Rt ---1
F R, t I P = IV
୔ ଵଵ଴௫ଵ଴య
I = ୚ = ଶଶ଴ = 500 A
F I 1 , W = (500)2x0.2x10
‫ ׵‬W = 500,000 J Ans
. V = 220,000 , W = ?
W = I2Rt ---1
F R, t I P = IV
୔ ଵଵ଴௫ଵ଴య
I = ୚ = ଶଶ଴,଴଴଴ = 0.5 A
F I 1 , W = (0.5)2x0.2x10
‫ ׵‬W = 0.5 J Ans
- F F F ˂ F F F F
F F F F F
˂ 3 F ˂ F ˈ F
F ˂ ˈ F F F F F
˂ 230,000 F F F F ˂ F 69,000 F F F
F F F 220 F F F F F F
F ˂
F ˆ F www.schoolDD.com 9

11. 17.3 F ˂ (Transformer)
F F
I2
F F I1 F
R E2
E1 N1 N2
I1 I2
N1 N2
F F
F ˂ ˈ F F F F F ˂ F
F ˂ F
F
F ˂ I1 ˂ E1 F F
F F ( I1 ˂ F ) F F F
F F ˂ E2 ˂
I2 F ˂ F
۳૚ ‫ۼ‬ ୚భ ୒
۳૛
= ‫ۼ‬૚ ୚మ
= ୒భ
మ
૛
V1 V2 ˈ F F F
F ˂ 2
1. F ( N2 > N1 F E2 > E1 ) N1 N2
2. F ( N2 < N1 F E2 < E1 )
N1 N2
F F F ˂
F F F
F F F F
˂ W1 = ˂ W2
F ˆ F www.schoolDD.com 10

12. P1 = P2 I1V1 = I2V2
P1 = ˂ F
P2 = ˂
(Eddy current)
ˈ ˂ F F
F ˈ F F F
˂ F ˂ F F F ˂ ( P2 < P 1 )
˂ ˈ F F
F F F F F F F F F
F F F
F ˂
1. F ˂ F F
2. F F F F F ʽ - ʽ ˈ F F
୉ ୒ ୚
3. ୉భ = ୒భ = ୚భ
మ మ మ
4. F N2 > N1 , E2 > E1
F N2 < N1 , E2 < E1
5. P1 = P2
F 4
F 200 50 F
˂ 12 F ˂ F 0.5 F F F
˂ F F
I1 = 0.5
I2 = ?
E1 = 12
N1 = 200 N2 = 50
୉భ ୒
୉మ
= ୒భ
మ
E 2 = E 1 ሺ N1 ሻ
N 2
50
= 12ሺ200ሻ
F ˆ F www.schoolDD.com 11

13. ‫ ׵‬E2 = 3 V = V2
P 1 = P2
I1V1 = I2V2
V1 = E1 , V2 = E2
F F 0.5x12 = I2x2
‫ ׵‬I2 = 2 A Ans
F 5
F 20 100 F F
F 25 F F F ˂ F 20 F F ˂ F F
25 F F
E1 = 20 R = 25 Ω
N1 = 20 N2 = 100
˂ F F 25 F F F F ˈ F F ˈ
F F (W/ Q) F F
W = QV
୛
‫ ׵‬V= ୕
E1 = V1 = 20 V
୉భ ୒
୉మ
= ୒భ
మ
E 2 = E 1 ሺ N1 ሻ
N 2
= 20ሺ100ሻ
20
‫ ׵‬E2 = 100 V
V = IR
୚మ
I2 = ୖ
ଵ଴଴
= ଶହ
‫ ׵‬I2 = 4 A Ans
F ˆ F www.schoolDD.com 12

14. 17.4 ˂ F F ˂
i R
V
AC
˂ i F Fv
Im Vm
0 t 0 t
T/2 T 3T/2 2T T/2 T 3T/2 2T
- Im - Vm
F R F ˂ AC ( F ) (i)
F F F F (v) F F F
ˈ ˆ F F ˈ
ω=
i = Im sin ࣓t ஘ ଶ஠
= = = 2ߨf
v = Vm sin ࣓t ୲ ୘
i v ˈ ˂ F F t
Im Vm ˈ ˂ F F
F
F F ˂ F F ˂
v = iR
V m = Im R
˂ ˂
˂ ˂ (p) ˂ F
F ˆ F www.schoolDD.com 13

15. p = iv
Pm = Im Vm
F i, F Fv, ˂ p t ˂
i,v, p
Pm p p , Pm ˈ i v
Vm v
Im
i t
0
- Im T/2 T
- Vm
FF F ˂ F F 1 F ˈ F F
˂ F ˈ
i,v
୧ ା୧ F
i +
i = =0 ( +,-)
0 t ୴
ଶ
ା୴ F
v - T v = ଶ
=0
p ୔
p = ଶౣ
Pm p=iv
p
= ½ ImVm
୚ౣ
t = ½ Im(Im R) = ½ ( ୖ )Vm
0
T
ଵ ଵ ୚మ
p = ଶ Im2 R = ଶ ୖ
ౣ
i v
Im Vm
0 t 0 t
- Im - Vm
i2 v2
Im 2 Vm2
i2 = Im2 /2 v2 = Vm2 /2
t t
0 0
T T
F ˆ F www.schoolDD.com 14

16. FF
(i2) = ½ Im2 (v2) = ½ Vm2
୍ౣ
F F Irms = ඥሺiଶሻ = √ଶ
ˈ F ˂
୚ౣ
Vrms = ඥሺv ଶ ሻ = √ଶ
ˈ F F F
F ˂ F
୔ౣ ୍ౣ ୚
p = ଶ
= ½ ImVm = √ଶ
x √ౣ = Irms Vrms
ଶ
F Irms Vrms F F F F ˈ F F F F F ˂
F F ˂ F F F F I V ˂
˂, F F ˂ ˂
1. i = Im sin ߱t (Im = )
F F v = Vm sin ߱t (Vm = F F )
2. F F F F (V = IR)
v = iR
Vm = ImR
3. ˂ F F ˂ (P = IV)
p = iv
Pm = Im Vm
୔ౣ ୍ ୚
p = ଶ = ౣଶ ౣ = IrmsVrms
4. F
୍
Irms = √ౣଶ
୚ౣ
Vrms = √ଶ
F 6
˂ ˂ i t i = 2 sin (314t)
. ˂
.
. F Irms
i = Im sin ߱t
F i = 2 sin (314t )
F ˆ F www.schoolDD.com 15

17. 2 F
˂ Im = 2 A Ans
߱ = 314
2πf = 314
ଷଵସ
f = ଶ୶ଷ.ଵସ = 50 Hz Ans
୍ౣ ଶ
Irms = √ଶ
= √ଶ
= √2 A Ans
F 7
40 F , 220 F F F F ˂ 220 F
. F
. ˂ F
. ˂
. ˂ 40 W , 220 V
i
AC
Vrms = 220
. F R
p = 40 W , Vrms = 220 V
୚
P = IV = ሺୖሻV
୚మ
= ୖ
୚మ ଶଶ଴మ
R= ୮
౨ౣ౩
= ସ଴
‫ ׵‬R = 1210 Ω Ans
. ˂ F Im
୍
Irms = √ౣ
ଶ
Im = √2 Irms
= √2 Irms
୚
= √2 ሺ ౨ౣ౩ሻ
ୖ
ଶଶ଴
= √2 ሺଵଶଵ଴ሻ
‫ ׵‬Im = 0.26 A Ans
F ˆ F www.schoolDD.com 16

18. . ˂ Pm
Pm = ImVm
= Im(√2 Vrms)
= 0.26(√2 x220)
‫ ׵‬Pm = 80 W Ans
. ˂ p
୔ౣ
p = ଶ
଼଴
= ଶ
‫׵‬p = 40 W Ans
F 8
˂ F F F F F F F F 220 F F F
F F F 10 F F F ˂
F Vrms = 220 V Irms = 10 mA
୚
Vm Vrms = √ౣ ଶ
Vm = √2 Vrms = √2 x220
‫ ׵‬Vm = 311 V Ans
୍
Im Irms = √ౣଶ
Im = √2 Irms = √2 x10
‫ ׵‬Im = 14 mA Ans
17.5
C i,v
i
iC iC vC F 90°
0 t
V vC
AC
. F i,v t
F C F ˂ F ˂ F iC
గ
F F F vC F 90° ଶ
F ˆ F www.schoolDD.com 17

19. i,v
i L
0 vL t
V
iL
AC
F L F ˂ F F F vL F
గ
F iL F 90° ଶ
.
F R,L,C
p
v = Vm sin ߱t i,v p=iv
Pm
R i = Im sin ߱t Im Vm t t
i v p = iv
Pm = ImVm i v
p = Pm/2
p
C i,v p=iv
v = Vm sin ߱t Pm
Im , Vm i
t t
i v i = Im sin (߱t + π/2) v
p = iv గ
i v Fଶ
Pm = ImVm/2
p =0
p
L v = Vm sin ߱t i,v p=iv
Pm
i v Im , Vm v t t
i = Im sin (߱t - π/2)
i
p = iv
గ
Pm = ImVm/2 v i Fଶ
p =0
F ˆ F www.schoolDD.com 18

20. F
F ( XC ) F F
( XL ) F F ˈ F F F
F
୚
F R= ୍
୚౨ౣ౩
XC = ୍౨ౣ౩
୚౨ౣ౩
XL = ୍౨ౣ౩
F XC XL F FF F ˂ f F
C F L F
ଵ ଵ
XC = ఠେ
= ଶ஠୤ େ
XL = ߱L = 2ߨf L
f= F ˂ ( F )
C= ( )
L= ( )
F 9
˂ F F F F F
˂ F 10 F F F F F F F F
F 8.0 , 12.0 6.0 F F F
F
R C L
i
R,C,L F F F 10 mA F ‫ ׵‬Irms = 10
mA
F Vrms = 8 V
F ˆ F www.schoolDD.com 19

21. ୚౨ౣ౩ ଼
R R= ୍౨ౣ౩
= ଵ଴୶ଵ଴షయ
‫ ׵‬R = 800 Ω Ans
Vrms = 12 V
୚ ଵଶ
XC XC = ୍ ౨ౣ౩ = ଵ଴୶ଵ଴షయ
౨ౣ౩
‫ ׵‬XC = 1200 Ω Ans
Vrms = 6 V
୚ ଺
XL XL = ୍ ౨ౣ౩ = ଵ଴୶ଵ଴షయ
౨ౣ౩
‫ ׵‬XL = 600 Ω Ans
F 10
˂ 50 F F F rms ˂ 12 F F rms
˂ F ˂
. F F 10 F
. 33
. 20
. R
f = 50 Hz
Vrms = 12 V
୚
V = IR I= ୖ
୚ ଵଶ
Irms = ౨ౣ౩ = ଵ଴
ୖ
‫ ׵‬Irms = 1.2 A Ans
.
C = 33 ߤF
f = 50 Hz
Vrms = 12 V
F ˆ F www.schoolDD.com 20

22. ଵ ଵ ଵ
XC XC = ఠେ
= ଶ஠୤ େ
= ଶ୶ଷ.ଵସ୶ହ଴୶ଷଷ୶ଵ଴షల
XC = 96.5 Ω
୚౨ౣ౩ ଵଶ
Irms = ଡ଼ = ଽ଺.ହ
ి
‫ ׵‬Irms = 0.12 A Ans
.
L = 20 mH
f = 50 Hz
Vrms = 12 V
XL XL = ߱L = 2ߨf L = 2x3.14x50x20x10-3
XL = 6.28 Ω
୚౨ౣ౩ ଵଶ
Irms = ଡ଼ = ଺.ଶ଼
ై
‫ ׵‬Irms = 1.91 A Ans
17.6 ˂ F ˂ F
PHILIPS
F
F HR 3312
BLADE SIZE 300 mm (12 )
˂ VOLTAGE 220 V 50 Hz
˂ POWER 45 W
˂ AMPERE 0.25 A
F 0.83 m3/min/W
F ˂ F F ˂ F F ˂ F
F F ˈ F rms F ˂ ˈ ˂ (p ) F ˂ F
F F
p = IrmsVrmscos θ
θ F ˂ F F ˂
cos θ F ˂ F F 1 (θ = 0°)
F ˆ F www.schoolDD.com 21

23. - F i v = 0° --> cos θ = 1
θ
F i v F θ ് 0° --> cos θ < 1
˂ W t F
୛
p = ୲
W=p t
F ˂
F F F ˂ F (W) F F ˂ F
ˈ F F F (UNIT )
1 F = 1 F
F ˂ F F F F ( ) ˈ F
F F F
-p F ˂ F p F F p
F ˈ F
F 11
F F F 485 ˂ F F ˂ 220 F
. ˂ F F F i
. F F F
. ˂ F F ˈ 0.5 v = 220 W
. F . F F ˂ F F F F ˈ 3 F F
Fp = 485 W , Vrms = 220 V , t = 0.5x60x60 = 1800 s cos θ = 1.0
. Irms = ?
p = IrmsVrmscos θ
୮ ସ଼ହ
Irms = ୚ = ଶଶ଴ (cos θ = 1.0)
౨ౣ౩
‫ ׵‬Irms = 2.2 A Ans
. R=?
୚౨ౣ౩ ଶଶ଴
R= ୍౨ౣ౩
= ଶ.ଶ
‫ ׵‬R = 100 Ω Ans
F ˆ F www.schoolDD.com 22

24. . W=?
୛
= ୲ p
W = p t = 485x1800
‫ ׵‬W = 8.73x105 J Ans
. F ˂
F . W = 8.73x105 J (= F )
F F ˈ F (=1 F )
଼.଻ଷ୶ଵ଴ఱ
W = ଵ଴య୶଺଴୶଺଴
W = 0.24 F = 0.24 F
‫ ׵‬F F 3x0.24 = 0.72 Ans
F 12
˂ ˂ i ˈ i = 5 sin (߱t - 40°) F F ˈ v = 15 sin (߱t +
20°)
.
. ˂ F F F
F i = 5 sin (߱t - 40°) v = 15 sin (߱t + 20°) FF v i F 20-(-40) = 60° Im =
5 A , Vm = 15 ( i = Im sin ߱t v = Vm sin ߱t)
. cos θ = ? , θ = 60°
cos θ = cos 60°
‫ ׵‬cos θ = ½ = 0.5 Ans
.p =?
p = IrmsVrms cos θ
୍ ୚ ହ ଵହ ଵ ଻ହ
= √ౣ x √ౣ x cos 60 =
ଶ ଶ
x x =
√ଶ √ଶ ଶ ସ
‫׵‬p = 18.75 W Ans
F 13
˂ I1 , I2 I3 ˂ F F ˂
I2 I1
ʽˊ ˆ
120 V 40 W
800 W
40 W
I3 y x
F ˆ F www.schoolDD.com 23

25. F ˂ F F F F F ˂ F F
Vrms = 120 V
F F F ˂ F F p = IrmsVrms
୮
Irms = ୚౨ౣ౩
ସ଴ ଵ
y = ଵଶ଴ = ଷ A
଼଴଴ ଶ଴
x = ଵଶ଴ = ଷ A
ସ଴ ଵ
I1 = ଵଶ଴ = ଷ A Ans
ଶ଴ ଵ
I2 = x + I1 = ଷ + ଷ = 7 A Ans
ଵ ଶ଴ ଵ
I3 = y + x + I1 = ଷ + ଷ + ଷ = 7.33 A Ans
17.7 ˂ F
N N
L L L
L
F ˂ 3 4
N L
F
ʽ F
L N
N
L
L
N
N L
˂
F
F ˂ F
F ˆ F www.schoolDD.com 24