# 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

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

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

# Example 1: Parallel Plates

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

Assume +Q and -Q

# Example 2: Cylindrical Capacitor

- Assume +Q and -Q

# Example 3: Spherical Capacitor

- Assume +Q and -Q

# Energy Stored in a Capacitor

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

# Field Energy Density

# Dielectrics

Insulating Materials

# Dielectric Constant (κ)

# Example 4: Capacitors in Series

Determine the equivalent capacitance of two capacitors in series

# Example 5: Capacitors in Parallel

Determine the equivalent capacitance of two capacitors in parallel

# 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?

# 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