capacitance van de graaff generator static charge generator
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Capacitance
Van de Graaff Generator
Static Charge Generator
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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.
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Capacitance
Van de Graaff Generator
Mathematically, Capacitance is this way:
CVQ
VQ
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Capacitance
Van de Graaff Generator
Mathematically, Capacitance is this way:
CVQ
VQ
FaradV
QC
C
Volt
Coul
Voltage
Charge
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Capacitance
Van de Graaff Generator
The greater the capacitance, the greater the amount of charge that can be stored.
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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
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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
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Capacitance
Van de Graaff Generator
What limits how many charges the dome can hold?
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Capacitance
Van de Graaff Generator
What limits how many charges the dome can hold?
Repulsion
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Capacitance
Van de Graaff Generator
What limits how many charges the dome can hold?
We can’t force any more electrons on the dome
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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?
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Capacitance
A bigger dome is one solution. We can fit more electrons.
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Capacitance
But there’s another solution…
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Capacitance
Introduce another generator with the opposite charge
What will that make the electrons do?
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Capacitance
As they move closer…
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Capacitance
The charges attract…
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Capacitance
And the charges become more concentrated…leaving room for?
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Capacitance
And the charges become more concentrated…leaving room for? MORE CHARGES!
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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.
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Capacitance
More typically, a capacitor is a “parallel plate” capacitor:
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Capacitance
More typically, a capacitor is a “parallel plate” capacitor:
Let’s place insulating material between the plates
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Capacitance
More typically, a capacitor is a “parallel plate” capacitor:
Press the plates closer together…
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Capacitance
More typically, a capacitor is a “parallel plate” capacitor:
Press the plates closer together…
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Capacitance
More typically, a capacitor is a “parallel plate” capacitor:
Then roll them up…
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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
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Capacitance
Recall our definition of work (area under the curve)
Charge, Q
Voltage
Charge, Q
Voltagearea
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Capacitance
Charge, Q
Voltagearea
Area = ?
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Capacitance
Charge, Q
Voltagearea
Area = ½ bh
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Capacitance
Charge, Q
Voltagearea
Area = ½ bh = ½ VQ = ½ (Q/C)Q = C
Q2
21
C
QPE
2
21
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Capacitance
Variations:
QVPE
CVPE
C
QPE
21
221
2
21
Prove that 2 and 3 follow from 1
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Capacitance
QVPE
CVPE
C
QPE
21
221
2
21
Show that each of these formulas ends up in Joules
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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.
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Capacitance
Answers:
1.182 J
2.188 J
3.0.22 J