# Worksheet: Capacitor Charging and Discharging

In this worksheet, we will practice calculating instantaneous current, charge, and voltage in circuits containing a resistor and a capacitor.

**Q1: **

What is the time constant of the circuit shown in the diagram? Answer to three significant figures.

**Q2: **

A circuit with a resistance of 42 Ω and a capacitance of 540 µF is powered by a 3.4 V battery. How much time after the capacitor starts being charged is the instantaneous current in the circuit 15 mA?

**Q3: **

A resistor–capacitor circuit powered by a 12.6 V battery has a time constant of 177 ms. How much time must the capacitor be charged for to have a potential difference of 9.30 V across it?

**Q4: **

What is the time constant of a circuit with a resistance of 7.5 kΩ and a capacitance of 450 µF?

**Q5: **

A resistor–capacitor circuit is powered by a 9.5 V battery. The initially uncharged capacitor is charged for 320 ms, after which the instantaneous potential difference across it is 5.5 V. What is the time constant of the circuit?

**Q6: **

A resistor–capacitor circuit powered by an 8.20 V battery has a time constant of 156 ms. The initially uncharged capacitor is charged for 215 ms. What is the potential difference across the capacitor after that time?

**Q7: **

What resistance would be needed in a circuit that contains a 6.75 µF capacitor for the time constant of the circuit to be 0.125 ms?

**Q8: **

A 975 µF capacitor is initially fully charged in a circuit that has a 12.5 V battery and a 115 Ω resistance. The ends of the circuit that are connected to the terminals of the battery are then connected directly to each other and the capacitor is discharged for one time constant of the circuit.

What is the instantaneous potential difference across the capacitor at the end of the discharging interval?

What is the instantaneous current in the circuit at the end of the discharging interval?

**Q9: **

A 175 µF capacitor is fully charged by a 25 V battery and is then discharged. What is the charge stored in the capacitor after two time constants of the circuit have passed since discharging began?

- A C
- B C
- C C
- D C
- E C

**Q10: **

The graph shows the change in current against time of a circuit in which a capacitor is discharging. After the capacitor has been discharging for 1.25 s, the ratio of the initial current to the instantaneous current is . The capacitor has a capacitance of 25 µF. What is the resistance of the circuit?

**Q11: **

A 225 µF capacitor is discharged in a circuit that has a 15.0 V source and a 1,350 Ω resistance. What is the average power output from the capacitor while it discharges from a fully charged state for three time constants of the circuit?