# 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?

- A 0.019 s
- B 0.032 s
- C 0.038 s
- D 0.076 s
- E 0.014 s

**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?