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Capacitance
Van de Graaff Generator
Static Charge Generator
Capacitance
Van de Graaff Generator
Let’s say it generates negative charges…
Capacitance is a measure of how much charge can be stored on a device.
Capacitance
Van de Graaff Generator
Mathematically, Capacitance is this way:
CVQ
VQ
Capacitance
Van de Graaff Generator
Mathematically, Capacitance is this way:
CVQ
VQ
FaradV
QC
C
Volt
Coul
Voltage
Charge
Capacitance
Van de Graaff Generator
The greater the capacitance, the greater the amount of charge that can be stored.
Capacitance
Van de Graaff Generator
Let’s see how much charge is on the Van de Graaff generator. The voltage is rated as 400,000 V:
C 00001016.0
)99(
)2286(. 400,000
)2286(.
)99( volts000,400
2
2
2
2
CJ
Q
QE
m
m
QE
r
kQV
CNm
CNm
Capacitance
Van de Graaff Generator
What is the Capacitance of the Van de Graaff generator?
pFC
FaradsC
volts
coulC
V
QC
4.25
1054.2
000,400
1016.10
11
6
Capacitance
Van de Graaff Generator
What limits how many charges the dome can hold?
Capacitance
Van de Graaff Generator
What limits how many charges the dome can hold?
Repulsion
Capacitance
Van de Graaff Generator
What limits how many charges the dome can hold?
We can’t force any more electrons on the dome
Capacitance
Van de Graaff Generator
What limits how many charges the dome can hold?
We can’t force any more electrons on the dome
Solutions?
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’)
qVW
The incremental increase in Work is:
qVWPE
qVW
Capacitance
Recall our definition of work (area under the curve)
Charge, Q
Voltage
Charge, Q
Voltagearea
Capacitance
Charge, Q
Voltagearea
Area = ?
Capacitance
Charge, Q
Voltagearea
Area = ½ bh
Capacitance
Charge, Q
Voltagearea
Area = ½ bh = ½ VQ = ½ (Q/C)Q = C
Q2
21
C
QPE
2
21
Capacitance
Variations:
QVPE
CVPE
C
QPE
21
221
2
21
Prove that 2 and 3 follow from 1
Capacitance
QVPE
CVPE
C
QPE
21
221
2
21
Show that each of these formulas ends up in Joules
Capacitance
QVPE
CVPE
C
QPE
21
221
2
21
3. Find the energy stored in a capacitor were C = 12 x 10-6 F and Q = 2.3 x 10-3 C.
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.
Capacitance
Answers:
1.182 J
2.188 J
3.0.22 J
