# 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?