The Physics
Hypertextbook
Opus in profectus

# Capacitors in Circuits

## Problems

### practice

1. Write something.
2. Write something.
3. Write something.
4. Write something completely different.

### numerical

1. A 12 V battery is connected to two resistors and two capacitors as shown in the diagram on the right. The resistors and the capacitors were chosen so that points A and B are at the same potential. Determine…
1. the potential drop across the 1 Ω resistor
2. the potential drop across the 3 Ω resistor
3. the current through the 1 Ω resistor
4. the current through the 3 Ω resistor
5. the potential drop across the 1 μF capacitor
6. the potential drop across the unknown capacitor
7. the charge stored in the 1 μF capacitor
8. the charge stored in the unknown capacitor
9. the capacitance of the unknown capacitor
2. The circuit below is made of three 2 Ω resistors, three 2 μF capacitors, and a 12 V battery. There is a rotating switch at the top and bottom of the circuit made out of wire in the shape of a "T". Initially, all capacitors are uncharged and both switches are midway between two positions.

currents through… charges on…
R1 R2 R3 C1 C2 C3
initial conditions 0 A 0 A 0 A 0 μC 0 μC 0 μC

The two switches are then simultaneously rotated into a series of three positions, one after the other, and held there for a "long time". For each position, determine the current through each resistor and the charge on each capacitor at the moment the circuit is completed and then after a "long time".

1. First position

First position
currents through… charges on…
R1 R2 R3 C1 C2 C3
circuit completed
after a long time
2. Second position

Second position
currents through… charges on…
R1 R2 R3 C1 C2 C3
circuit completed
after a long time
3. Third position

Third position
currents through… charges on…
R1 R2 R3 C1 C2 C3
circuit completed
after a long time