The document discusses capacitors and capacitance. It defines a capacitor as a device that stores electric potential energy and electric charge using two conductors separated by an insulator. It explains the concepts of capacitance, capacitors in series and parallel, and provides examples of calculating capacitance and stored energy for parallel plate capacitors.

1. SIR JOHNEL V.
ESPONILLA
GENERAL PHYSICS II

2. CAPACITORS AND
CAPACITANCE
CAPACITORS IN SERIES AND
PARALLEL
EXAMPLE
S

4. device that stores
electric potential
energy and electric
charge
Two conductors
separated by an
insulator form a
capacitor.
The net charge on a
capacitor is zero.
To charge a capacitor,
wires are connected to
the opposite sides of a
battery.
This gives a fixed
potential difference Vab
= voltage of battery.
CAPACITANCE:
constant equal to the
ratio of the charge on
each conductor to the
potential difference
between them
𝑪 =
𝑸
𝑽𝒂𝒃
CAPACITANCE:
Units: 1 Farad (F)
= Q/V = C2/J = C2/Nm

5. PARALLEL PLATE
CAPACITOR:
Uniform electric field
between the plates,
charge uniformly
distributed over
opposite surfaces
𝐸 =
𝑄
𝜀0𝐴
𝑉𝑎𝑏 = 𝐸 ∗ 𝑑 =
1
𝜀0
𝑄𝑑
𝐴
C=
𝑄
𝑉𝑎𝑏
= 𝜀0
𝐴
𝑑

6. CAPACITORS IN
SERIES:
Same charge (Q).
𝑉𝑎𝑏 = 𝑉
𝑎𝑐 + 𝑉𝑐𝑏
𝐶𝑒𝑞 =
𝑄
𝑉𝑎𝑏
=
𝑄
𝑉1 + 𝑉2
1
𝐶𝑒𝑞
=
𝑉1
𝑄
+
𝑉1
𝑄
=
1
𝐶1
+
1
𝐶2

7. CAPACITORS IN
PARALLEL:
Same potential V, different
charge.
𝑄1 = 𝐶1 𝑉1 𝑄2 = 𝐶2 𝑉2
𝑄 = 𝑄1 + 𝑄2
𝐶𝑒𝑞 =
𝑄
𝑉𝑎𝑏
=
𝑄1+𝑄2
𝑉
𝐶𝑒𝑞 =
𝑄1
𝑉
+
𝑄2
𝑉
= 𝐶1+ 𝐶2

8. Consider a parallel-plate capacitor that is about the
size of your fingernail. The plates are squares with
edges of length L = 1.0 cm, separated by d=10𝜇m,
which is about the diameter of human air. a.) Find the
capacitance.
b.) If the potential across the capacitor is ∆V = 12 V,
what is the energy stored?
𝑺𝑲𝑬𝑻𝑪𝑯 𝑮𝑰𝑽𝑬𝑵 𝑼𝑵𝑲𝑵𝑶𝑾𝑵
𝑺𝑶𝑳𝑼𝑻𝑰𝑶𝑵 𝑭𝑰𝑵𝑨𝑳 𝑨𝑵𝑺𝑾𝑬𝑹

9. Consider a parallel-plate capacitor that is about the size of your fingernail. The plates are squares
with edges of length L = 1.0 cm, separated by d=10𝜇m, which is about the diameter of human air.
a.) Find the capacitance.
b.) If the potential across the capacitor is ∆V = 12 V, what is the energy stored?
𝑺𝑲𝑬𝑻𝑪𝑯 𝑮𝑰𝑽𝑬𝑵
L = 1.0 cm or 0.010 m
d = 10 𝜇m or 10 x 10-5 m
𝜀0 = 8.85 𝑥 10 − 12 C2/Nm2
UNKNOWN
C

10. Consider a parallel-plate capacitor that is about the size of your fingernail. The plates are squares
with edges of length L = 1.0 cm, separated by d=10𝜇m, which is about the diameter of human air.
a.) Find the capacitance.
b.) If the potential across the capacitor is ∆V = 12 V, what is the energy stored?
𝑺𝑶𝑳𝑼𝑻𝑰𝑶𝑵
𝐶 = 𝜀0
𝐴
𝑑
= 𝜀0
𝐿2
𝑑
C =
(8.85 𝑥
10−12𝐶2
𝑁𝑚2 )(0.010𝑚)2
(1.0𝑥10−5𝑚)
C = 8.9 x 10-11 F
𝑭𝑰𝑵𝑨𝑳 𝑨𝑵𝑺𝑾𝑬𝑹

11. Consider a parallel-plate capacitor that is about the size of your fingernail. The plates are squares
with edges of length L = 1.0 cm, separated by d=10𝜇m, which is about the diameter of human air.
a.) Find the capacitance.
b.) If the potential across the capacitor is ∆V = 12 V, what is the energy stored?
𝑺𝑲𝑬𝑻𝑪𝑯 𝑮𝑰𝑽𝑬𝑵
C = 8.9 X 10-11 F
∆V = 12 V
UNKNOWN
PEcap

12. Consider a parallel-plate capacitor that is about the size of your fingernail. The plates are squares
with edges of length L = 1.0 cm, separated by d=10𝜇m, which is about the diameter of human air.
a.) Find the capacitance.
b.) If the potential across the capacitor is ∆V = 12 V, what is the energy stored?
𝑺𝑶𝑳𝑼𝑻𝑰𝑶𝑵
𝑃𝐸𝑐𝑎𝑝 =
1
2
𝐶(∆𝑉)2
𝑃𝐸𝑐𝑎𝑝 =
1
2
(8.9𝑥10−11
)(12𝑉)2
PEcap = 6.4 x 10-9
J
𝑭𝑰𝑵𝑨𝑳 𝑨𝑵𝑺𝑾𝑬𝑹

13. Modern computer memories use parallel-plate capacitors to store
information, and these capacitors are the basic elements of a random-
access memory (RAM) chip. Assume one of these capacitors has
plates with area L x L, where L = 1.0 x 10-7m, and a plate separation
d = 10 nm.
a.) Find the capacitance of such a capacitor.
b.) Calculate the amount of charge that must be placed onto the
plates to obtain a potential difference of 5.0 V across them.
c.) How many electrons does this charge correspond to?
𝑺𝑲𝑬𝑻𝑪𝑯 𝑮𝑰𝑽𝑬𝑵 𝑼𝑵𝑲𝑵𝑶𝑾𝑵
𝑺𝑶𝑳𝑼𝑻𝑰𝑶𝑵 𝑭𝑰𝑵𝑨𝑳 𝑨𝑵𝑺𝑾𝑬𝑹

14. Four capacitors are connected. If all have the same capacitance
(C1=C2=C3=C4=C), what is the equivalent capacitance of this
combination?
𝑺𝑲𝑬𝑻𝑪𝑯 𝑮𝑰𝑽𝑬𝑵 𝑼𝑵𝑲𝑵𝑶𝑾𝑵
𝑺𝑶𝑳𝑼𝑻𝑰𝑶𝑵 𝑭𝑰𝑵𝑨𝑳 𝑨𝑵𝑺𝑾𝑬𝑹
C1
C2
C3
C4
C12=2C C34=2C
Cequiv=C

15. 1. A voltage of 12 V is placed on a capacitor with C = 100 pF.
a.) What is the charge on the capacitor?
b.) How much energy is stored in the capacitor?
2. Two capacitors with C1=1.5𝜇F are connected in parallel. If the combined
charge on both capacitors is 25 𝜇F, what is the voltage across the capacitor?
3. A parallel-plate capacitor has square plates of edge length 1.0 cm and a plate
spacing of 0.10 mm. If the gap between the plates is filled with mica, what is the
capacitance?
𝑺𝑲𝑬𝑻𝑪𝑯 𝑮𝑰𝑽𝑬𝑵 𝑼𝑵𝑲𝑵𝑶𝑾𝑵
𝑺𝑶𝑳𝑼𝑻𝑰𝑶𝑵 𝑭𝑰𝑵𝑨𝑳 𝑨𝑵𝑺𝑾𝑬𝑹