phy1020.DVI

Figure 25.1: Electric field between the plates of a parallel-plate capacitor. The electric field between the
plates is uniform, except near the edges. (©GNU-FDL, Wikimedia Commons [11].)

To find the capacitance, we divide this into the charge on each plate,Q:

CD

Q

V

D

" 0 A

d

: (25.5)

Note that the capacitance dependsonlyon the geometry of the capacitor (plate area and spacing), and not
on the charge on capacitor or the voltage between the plates. This is true of other capacitor configurations
as well:Cdepends only on the geometrical properties of the capacitor. Note also that the parallel-plate
capacitor has a larger capacitance if the plates are larger, or if the plates are closer together.

25.2 Capacitors in Series and Parallel

If several capacitors are connected end-to-end (in series), the equivalent resistance is equal to the reciprocal
of the sum of the reciprocals of the individual resistances:

1

Cs

D

X

i

1

Ci

(25.6)

D

1

C 1

C

1

C 2

C

1

C 3

C (25.7)

A common error in computing series capacitances is to compute sum of the reciprocals of the individual
capacitances, then forget to take the reciprocal of the result at the end. Be careful not to do this!
If the capacitors are connectedin parallel, the the equivalent capacitance is the sum of the individual
capacitances:

CpD

X

i

Ci (25.8)

DC 1 CC 2 CC 3 C (25.9)