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Mastering Capacitance: Definitions, Calculations & Examples

Understand the fundamental concepts of capacitance, including definitions, calculations, dielectrics, and practical examples for various geometries like parallel plates, spheres, and cylinders. Gain insights into capacitance properties and formulas.

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Mastering Capacitance: Definitions, Calculations & Examples

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  1. Capacitance (Chapter 26) Capacitance – the property of a conductor or set of conductors and insulators to store electric chargeCapacitor – an electronic component that has the ability to store charge • Definition • Calculating Capacitance • Dielectrics and Dielectric Constant

  2. Definition: Capacitance C of two conductors with equal but opposite charges V = potential difference created when charge +Q is on one conductor, and –Q is on the other. Unit: Typically ranges from 1μF = 10-6 F and 1pF = 10-12 F 1 F is a LOT of stored charge !!!

  3. Finding C for Symmetrical Charges 1) Find the electric field as a function of r using Gauss’s Law. 2) Choose a path along a field line: the potential change with each small change dr in distance is dV =- E(r)dr 3) Integrate from start to end of field line to find the potential difference. 4) C=Q/V

  4. d +Q -Q Recall … (between plates) (uniform ) Example 1: Parallel Plates area A, separation d Surface charge densities: Hence, C depends only on the geometry of the plates

  5. d +Q -Q Quiz: As the plates are moved apart, which of the following will increase, decrease, or stay the same? • Electric field between the plates • Electric potential difference between the plates • Capacitance of the plates

  6. Example 2: Sphere What is the capacitance of an isolated sphericalconductor of radius R and charge Q?

  7. R1 R2 Example 3: Concentric Spheres Derive: -Q +Q

  8. Find capacitances of… Examples: • 2 sheets of foil, 25 cm x 40 cm, 1 mm apart (in air.) • The earth and the ionosphere (height: 100 km) as a pair of concentric spheres.

  9. Example 4: Concentric Cylinders -Q R2 +Q R1 L For L >> R2, show:

  10. Solution:

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