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Capacitance
Static Charge Generator
Van de Graaff Generator
Capacitance
Let’s say it generates
negative charges…
Capacitance is a
measure of how
much charge can be
stored on a device.
Van de Graaff Generator
Capacitance
Mathematically,
Capacitance is this way:
Q V
Q  CV
Van de Graaff Generator
Capacitance
Mathematically,
Capacitance is this way:
Q V
Q  CV
Van de Graaff Generator
Charge
C
Voltage
Q Coul
C 
 Farad
V Volt
Capacitance
The greater the
capacitance, the
greater the amount of
charge that can be
stored.
Van de Graaff Generator
Capacitance
Let’s see how much
charge is on the Van
de Graaff generator.
The voltage is rated as
400,000 V:
kQ
V
r
400,000 volts 
Van de Graaff Generator
(9 E 9
Nm 2
C2
)Q
(.2286m)
400,000 CJ (.2286m)  Q
Nm 2
(9 E 9 C 2 )
Q  0.00001016 C
Capacitance
What is the Capacitance
of the Van de Graaff
generator?
Q
C
V
6
10.16  10 coul
C
400,000volts
11
C  2.54  10 Farads
C  25.4 pF
Van de Graaff Generator
Capacitance
What limits how many
charges the dome can
hold?
Van de Graaff Generator
Capacitance
What limits how many
charges the dome can
hold?
Repulsion
Van de Graaff Generator
Capacitance
What limits how many
charges the dome can
hold?
We can’t force any
more electrons on the
dome
Van de Graaff Generator
Capacitance
What limits how many
charges the dome can
hold?
We can’t force any
more electrons on the
dome
Solutions?
Van de Graaff Generator
Capacitance
A bigger dome is one
solution. We can fit
more electrons.
Capacitance
But there’s another solution…
Capacitance
Introduce another generator with the opposite charge
What will that make the electrons do?
Capacitance
As they move closer…
Capacitance
The charges attract…
Capacitance
And the charges become more concentrated…leaving
room for?
Capacitance
And the charges become more concentrated…leaving
room for? MORE CHARGES!
Capacitance
Capacitance is a measure of how much charge can be
stored on a device.
Our two van de Graaff generators constitute a what
is called a “capacitor”: two oppositely charged
conductors in close proximity.
Capacitance
More typically, a capacitor is a “parallel plate”
capacitor:
Capacitance
More typically, a capacitor is a “parallel plate”
capacitor:
Let’s place insulating
material between the
plates
Capacitance
More typically, a capacitor is a “parallel plate”
capacitor:
Press the plates
closer together…
Capacitance
More typically, a capacitor is a “parallel plate”
capacitor:
Press the plates
closer together…
Capacitance
More typically, a capacitor is a “parallel plate”
capacitor:
Then roll them up…
Capacitance
How much energy is stored in a capacitor?
We answer this by determining the WORK done in
forcing charges on to the plate (against the
repulsion of the voltage – increasing ‘q’)
W  qV
The incremental increase in Work is:
W  V q 
PE  W  V q 
Capacitance
Recall our definition of work (area under the
curve)
Charge, Q
Voltage
Charge, Q
Voltage
Capacitance
Charge, Q
Voltage
Area = ?
Capacitance
Charge, Q
Voltage
Area = ½ bh
Capacitance
Charge, Q
Voltage
2
Q
Area = ½ bh = ½ VQ = ½ (Q/C)Q = 12
C
2
Q
PE  12
C
Capacitance
Variations:
2
Q
PE 
C
2
1
PE  2 CV
1
2
PE  12 QV
Prove that 2 and 3
follow from 1
Capacitance
2
Q
PE 
C
2
1
PE  2 CV
1
2
PE  12 QV
Show that each of these
formulas ends up in Joules
Capacitance
2
Q
PE  12
C
PE  12 CV 2
PE  12 QV
1. Find the energy stored in a
capacitor where C = 50 F and
V = 2.7 volts.
2. Find the energy stored in a
capacitor where V = 5.00 volts
and Q = 75.0 C.
3. Find the energy stored in a
capacitor were C = 12 x 10-6 F
and Q = 2.3 x 10-3 C.
Capacitance
Answers:
1. 182 J
2. 188 J
3. 0.22 J