Chapter 25 Capacitors

25-2 Capacitor and Capacitance A capacitor consists of two isolated conductors (the plates) with charges + q and - q. Its capacitance C is defined from q=CV Where V is the potential difference between the conductors.

To find the capacitance, we have to find the electric field E, then the potential difference V. Gauss Law is used 25-3 Calculating the Capacitance

Parallel-Plate Capacitor The plate area is A and the distance between the plates is d.

Cylindrical Capacitor

Spherical Capacitor

The Capacity of an Isolated Conductor The isolated conductor is a sphere of conducting material which is isolated such that it keeps its charge. It is considered to be a spherical capacitor of an outer sphere with infinitely large radius b=∞ and substituting about b=infinity, and a=R, the radius of the inner sphere,we get

Sample Problem 25-1 In Fig a, switch S is closed to connect the uncharged capacitor of capacitance C =0.25 mF to the battery of potential difference V= 12V. The lower capacitor plate has thickness L=0.50 cm and face area A=2.0 x m 2, and it consists of copper, in which the density of conduction electrons is n= 8.49 x electrons/m 3. From what depth d within the plate (Fig. 25-7b) must electrons move to the plate face as the capacitor becomes charged?

25-4 Capacitances in Parallel and Series Parallel Connection

Series Connection

Sample Problem 25-2 a. Find the equivalent capacitance for the combination of capacitances shown in Fig a, across which potential difference V is applied. Assume C 1 = 12.0  F, C 2 = 5.30  F, and C 3 = 4.50  F. b.The potential difference applied to the input terminals in Fig. a is V=12.5 V. What is the charge on C 1 ?

Sample Problem 25-3 Capacitor 1, with C 1 =3.55  F, is charged to a potential difference V o = 6.30 V using a 6.30 V battery. The battery is then removed, and the capacitor is connected as in the figure to an uncharged capacitor 2, with C 2 =8.95  F When switch S is closed, charge flows between the capacitors. Find the charge on each capacitor when equilibrium is reached.

25-5 The Energy Stored in a Capacitor The potential energy U stored in a capacitor due to holding the charge q, is given by

The energy density u In case of the parallel plate capacitor, the potential energy per unit volume between the plates is given by

The capacity of this spherical conductor is given by Sample Problem 25-5 An isolated conducting sphere whose radius R is 6.85 cm has a charge q = 1.25 nC. a.How much potential energy is stored in the electric field of this charged conductor? b.What is the energy density at the surface of the sphere? and the potential energy is given by The energy density u is given by