Chapter 25

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# Chapter 25 - PowerPoint PPT Presentation

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. 25-3 Calculating the Capacitance.

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### 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.

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

Parallel-Plate Capacitor

The plate area is A and the distance between the plates is d.

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. 25-7 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 10-4 m2, and it consists of copper, in which the density of conduction electrons is n= 8.49 x 1028 electrons/m3. From what depth d within the plate (Fig. 25-7b) must electrons move to the plate face as the capacitor becomes charged?

Sample Problem 25-2

• Find the equivalent capacitance for the combination of capacitances shown in Fig a, across which potential difference V is applied. Assume C1 = 12.0 mF, C2 = 5.30 mF, and C3 = 4.50 mF.
• The potential difference applied to the input terminals in Fig. a is V=12.5 V. What is the charge on C1?

Sample Problem 25-3

Capacitor 1, with C1 =3.55 mF, is charged to a potential difference Vo= 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 C2=8.95 mF 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

Sample Problem 25-5

• An isolated conducting sphere whose radius R is 6.85 cm has a charge q = 1.25 nC.
• How much potential energy is stored in the electric field of this charged conductor?
• What is the energy density at the surface of the sphere?

The capacity of this spherical conductor is given by

and the potential energy is given by

The energy density u is given by