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C. Capacitance. Chapter 18 – Part II. Two parallel flat plates that store CHARGE is called a capacitor. The plates have dimensions >>d, the plate separation. The electric field in a parallel plate capacitor is normal to the plates. The “fringing fields” can be neglected.

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capacitance

C

Capacitance

Chapter 18 – Part II

slide2

Two parallel flat plates

that store CHARGE is

called a capacitor.

The plates have

dimensions >>d, the plate

separation.

The electric field in a

parallel plate capacitor

is normal to the plates.

The “fringing fields”

can be neglected.

Actually ANY physical

object that can store charge

is a capacitor.

slide3

V

A Capacitor Stores

CHARGE

Apply a Potential Difference V

And a charge Q is found on the

plates

Q

one way to charge
One Way to Charge:
  • Start with two isolated uncharged plates.
  • Take electrons and move them from the + to the – plate through the region between.
  • As the charge builds up, an electric field forms between the plates.
  • You therefore have to do work against the field as you continue to move charge from one plate to another.

The capacitor therefore stores energy!

slide8

The two metal objects in the figure have net charges of +79 pC and -79 pC, which result in a 10 V potential difference between them.

(a) What is the capacitance of the system? [7.9] pF(b) If the charges are changed to +222 pC and -222 pC, what does the capacitance become? [7.9] pF(c) What does the potential difference become?[28.1] V

parallel connection

V

CEquivalent=CE

Parallel Connection
series connection

q -q q -q

V

C1 C2

Series Connection

The charge on each

capacitor is the same !

example
Example

C1=12.0 uf

C2= 5.3 uf

C3= 4.5 ud

C1 C2

series

(12+5.3)pf

(12+5.3)pf

V

C3

a thunker
A Thunker

Find the equivalent capacitance between points a and b in the combination of capacitors shown in the figure.

V(ab) same across each

slide17

A capacitor is charged by being connected to a battery and is then disconnected from the battery. The plates are then pulled apart a little. How does each of the following quantities change as all this goes on? (a) the electric field between the plates, (b) the charge on the plates, (c) the potential difference across the plates, (d) the total energy stored in the capacitor.

stored energy
Stored Energy
  • Charge the Capacitor by moving Dq charge from + to – side.
  • Work = Dq Ed= Dq(V/d)d=DqV
we can measure the c of a capacitor later
We can measure the C of a capacitor (later)

C0 = Vacuum or air Value

C = With dielectric in place

C=kC0

messing with capacitors
Messing with Capacitors

The battery means that the

potential difference across

the capacitor remains constant.

For this case, we insert the dielectric but hold the voltage constant,

q=CV

since C  kC0

qk kC0V

THE EXTRA CHARGE COMES FROM THE BATTERY!

+

V

-

+

-

+

-

+

V

-

Remember – We hold V constant with the battery.

another case
Another Case
  • We charge the capacitor to a voltage V0.
  • We disconnect the battery.
  • We slip a dielectric in between the two plates.
  • We look at the voltage across the capacitor to see what happens.
no battery
No Battery

q0 =C0Vo

When the dielectric is inserted, no charge

is added so the charge must be the same.

q0

+

-

+

-

V0

V

qk

another way to think about this
Another Way to Think About This
  • There is an original charge q on the capacitor.
  • If you slide the dielectric into the capacitor, you are adding no additional STORED charge. Just moving some charge around in the dielectric material.
  • If you short the capacitors with your fingers, only the original charge on the capacitor can burn your fingers to a crisp!
  • The charge in q=CV must therefore be the free charge on the metal plates of the capacitor.
a little sheet from the past
A little sheet from the past..

-q’ +q’

-

-

-

+++

-q

q

0 2xEsheet 0