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Chapter 24 Capacitance
Capacitance
•  The capacitance is defined as the ratio of the charge
on one conductor of the capacitor to the potential
difference between the conductors.
•  Capacitor is a device that stores electrostatic
potential energy.
•  A capacitor consists of 2 spatially separated
conductors which can be charged to +Q and -Q.
•  Capacitance is measured in Faradays represented
by the letter F which is equal to (coulomb/volt)
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Capacitance between Parallel Plates
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Example
•  Calculate the capacitance. We assume +, - charge
densities on each plate with potential difference V:
d
A
++++
-----
What is the capacitance of a parallel plate
capacitor made out of two square plates 10
x10 cm2 separated by 1 mm wide gap?
A=0.01 m2
+++++++++++++++
d
- - - - - - - - - - - - - - -
C=
A
ε A
= o
4π kd
d
d=1 mm
If we connect 1.5V battery to its plates, how
much charge could be stored in this capacitor?
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Demos
Calculating Capacitance
1.  Put + Q , – Q on the plates.

2.  Find E between the plates i.e., given
the charges, using Gauss’ Law
3.  Find V across the plates
Q
4.  Use the definition C =
.
V
Demo: Capacitance versus d
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A Cylindrical Capacitor: Step 1
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A Cylindrical Capacitor : Step 2
•  The electric field in between the plates is radial.
Use a cylindrical shaped Gaussian surface of
radius R (R1<R<R2) of length l<<L
∫
S
 
E ⋅ dA =
∫ E dA + ∫ E dA =
R
Barrel
l
Endcaps
Qinside
εo
Where R1 < R2 << L
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A Cylindrical Capacitor : Step 3
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A Cylindrical Capacitor : Step 4
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Demo
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Energy Stored in a Capacitor
Demo: Energy stored in a capacitor
If a small amount of additional positive charge dq is transferred from the
negative conductor to the positive conductor through a potential
increase of V the potential energy of the charge and thus the capacitor
is increased by
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Demonstration: Energy Stored in a Capacitor
Energy stored in a capacitor
Energy stored in a capacitor:
U=
1
QΔV
2
Power supply (P.S.) supplies
voltage V.
Alternative equations for energy stored in a capacitor
Using
Using
Q = CΔV
ΔV =
Q
C
U=
1
2
C ( ΔV )
2
PEcap =
Q2
U=
2C
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P.S.
C
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CV 2
2
can produce a big jolt.
Application: defibrillator A fibrillating heart is one
in which the cardiac muscles go into uncontrolled
twitching and quivering. A defibrillator is used to
stop this.
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Numbers
U=
1
1
2
CV 2 = ( 70 µ F ) ( 5000 V ) = 875 J
2
2
About 200 J of this is sent through the
heart attack victim in 2 milliseconds.
P=
PE
200 J
=
= 100 kW
t
2 × 10 −3 s
short time
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