Capacitance and Capacitors

• Recall heat capacity (c) – The amount of heat energy (J) absorbed

(released) by a material of known mass (m) when changing temperature (T) with no phase change

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c =Q

mΔT

Electrical capacitance

• Defined as the amount of charge per volt that an object can hold

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C =Q

V

• Anything can be a capacitor

• The capacitance is defined as Q/V, but it is also solely dependent on the geometry of the capacitor. There should be an equation for the capacitance that is based only on the physical dimensions of the capacitor.

• The capacitance is measured in farads (F) after Michael Faraday

Example 1: A charged sphere of radius R

• If the charge on the sphere is Q, the potential at the surface is V = kQ/R

• The capacitance is then

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C =R

k= 4πε0R

Example 2: Parallel plate capacitor

• When the plates are charged, one plate has charge +Q, and the other -Q, so we say that the charge on the capacitor is Q.

• For parallel plates, V = Ed and E = 0, where = Q/A is the charge density on the plates, so

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C =ε0A

d

Figure 20-15The Effect of a Dielectric on the Electric Field of a Capacitor

Dielectric

• Adding a material to the space between the plates changes the capacitance of the capacitor

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C = κC0

Table 20-1Dielectric Constants

Substance Dielectric constant,

Water 80.4

Neoprene rubber 6.7

Pyrex glass 5.6

Mica 5.4

Paper 3.7

Mylar 3.1

Teflon 2.1

Air 1.00059

Vacuum 1

Figure 20-16Capacitance and the Computer Keyboard

Capacitors in series

•Adding capacitors in series,

•Vtot = V1 + V2, so

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1

Ctot=1

C1+1

C2+L

The charge on each capacitor must be the same when they are connected in series… Why?

Energy in capacitors

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UC =1

2QV =

1

2CV 2

W = qVave

Capacitors in parallel

Adding capacitors in parallel,

Vtot = V1 = V2, so

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Ctot =C1 +C2 +L

Sample problem

Charging capacitors in RC circuits

• When switch is first closed, uncharged capacitor acts like a wire, with no voltage drop across it (t = 0)

• After a long time, once the capacitor is fully charged, it acts like an open switch (t infinity)

• When switch is first closed on a charged capacitor, it acts like a battery