AP Physics

Capacitors in Series

C3

C2

C1

Capacitors in series share the same charge magnitude.

If C1 = 6 μF, C2 = 2 μF, and C3 = 3 μF, what is the equivalent capacitance Ceq of the circuit?

For capacitors connected in series the reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitances:

Notice that the equivalent capacitance is less than any of the individual

capacitances. This is true any time capacitors are connected in series.

Capacitors in Series

C3

C2

C1

Capacitors in parallel share the same potential difference.

Parallel Circuit

C3

C2C1

For capacitors connected in parallel the equivalent capacitance of the system is the sum of the capacitances of all the capacitors:

If C1 = 6 μF, C2 = 2 μF, and C3 = 3 μF, what is the equivalent capacitance Ceq of the circuit?

The equivalent capacitance of capacitors connected in parallel is always more than the capacitance

of any one capacitor.

Parallel Circuit

C3

C2C1

1. Find the charge stored and the voltage across each capacitor in the following circuit.

30 µF

180 V60 µF

90 µF

2. Find the energy stored in the circuit at equilibrium.

30 µF

180 V60 µF

90 µF

2. Find the energy stored in the circuit at equilibrium.

Find the equivalent capacitance.

30 µF

180 V60 µF

90 µF 180 V

Why do the charges flow?

When can they flow?

If the charges are always flowing from high potential to low potential how do they get at a higher potential to begin with?

Emf is not a force. It is an “energy per unit charge” quantity (just like potential).

Symbol: Units are _____________________________________

What supplies the emf?Batteries, generators, power supplies

These objects are like a water pump in a continuously flowing fountain

Ideal sources of emf have no internal resistance.

Most sources of emf are not ideal and have some internal resistance r.

Rε = Vtot

I

Vtot

I

Rr

ε

As a flashlight battery ages, its emf stays approximately constant, but its internal resistance increases. A fresh battery has an emf of 1.5 V and negligible internal resistance. When the battery needs replacement, its emf is still 1.5 V, but its internal resistance has increased to 1000 Ω. If this old battery is supplying 1.0 mA to a lightbulb, what is its terminal voltage?

Vtot

I

Rr

ε