What is a Capacitor?

• A capacitor is an electric device used to store electrical energy

  • Two conducting plates

  • Insulating material between (dielectric)

• Place opposite charges on each plate

• Develop a potential difference across the plates

• Energy is stored in the electric field between the plates

  

Capacitance

• Capacitance (C) is the ratio of the charge separated on the plates of a capacitor to the potential difference between the plates

• Units of capacitance are coulombs/volt, or farads (F)

  • A farad is a very large amount of capacitance

  

Calculating Capacitance

1. Assume a charge of +Q and -Q on each conductor

2. Find the electric field between the conductors (Gauss's Law)

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Example 1: Parallel Plates

• Determine the capacitance between identical parallel plates of area A separated by a distance d

1. Assume +Q and -Q

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Example 2: Cylindrical Capacitor

1. Assume +Q and -Q

Example 3: Spherical Capacitor

1. Assume +Q and -Q

Energy Stored in a Capacitor

• Work is done charging a capacitor, allowing the capacitor to store energy.

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Field Energy Density

Dielectrics

• Insulating Materials

  

  

Dielectric Constant (κ)

Example 4: Capacitors in Series

• Determine the equivalent capacitance of two capacitors in series

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Example 5: Capacitors in Parallel

• Determine the equivalent capacitance of two capacitors in parallel

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Example 6: Capacitance

• A capacitor stores 3 microcoulombs of charge with a potential difference of 1.5 volts across the plates. What is its capacitance? How much energy is stored in the capacitor?

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Example 7: Charge on a Capacitor

Example 8: Designing a Capacitor

Example 9: Calculating Capacitance

Example 10: Two Conducting Spheres

Example 11: Inserting a Dielectric