Capacitance Van de Graaff Generator Static Charge Generator.

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