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Chapter 25

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

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  1. Chapter 25 Capacitors

  2. 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.

  3. 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

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

  5. Cylindrical Capacitor

  6. Spherical Capacitor

  7. 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

  8. 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?

  9. 25-4 Capacitances in Parallel and Series Parallel Connection

  10. Series Connection

  11. 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?

  12. 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.

  13. 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

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

  15. 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

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