Worksheet: Charging and Discharging Multi-capacitor Circuits

In this worksheet, we will practice determining the charges and voltages of capacitors in multi-capacitor circuits when they charge and discharge.

Q1:

In a circuit, a capacitor is fully charged and then discharged through a different circuit that contains an uncharged capacitor. The discharging capacitor has greater capacitance than the charging capacitor. The potential difference across the capacitors is shown in the graph. Which of the following statements correctly compares the charge stored by the two capacitors when the current in the circuit is zero?

  • AThe charging capacitor stores the same charge as the discharging capacitor.
  • BThe charging capacitor stores more charge than the discharging capacitor.
  • CThe charging capacitor stores less charge than the discharging capacitor.

Q2:

The circuit shown in the diagram contains two capacitors in parallel. The capacitors are both fully charged.

What is the charge stored by the 18 µF capacitor?

  • A 1 . 3 × 1 0 C
  • B 1 . 5 × 1 0 C
  • C 5 . 9 × 1 0 C
  • D 1 1 × 1 0 C
  • E 5 . 5 × 1 0 C

What is the charge stored by the 44 µF capacitor?

  • A 1 . 3 × 1 0 C
  • B 5 . 5 × 1 0 C
  • C 5 . 9 × 1 0 C
  • D 1 . 5 × 1 0 C
  • E 1 . 9 × 1 0 C

Q3:

The circuit shown in the diagram contains two capacitors in series. The capacitors are both fully charged.

What is the potential difference across the 36 µF capacitor?

  • A 0.77 V
  • B 10 V
  • C 0.12 V
  • D 3.2 V
  • E 7.7 V

What is the potential difference across the 48 µF capacitor?

  • A 12 V
  • B 3.2 V
  • C 7.7 V
  • D 10 V
  • E 0.77 V

Q4:

The circuit shown in the diagram contains capacitors in series and in parallel. The capacitors are all fully charged.

How much charge is stored by the 10 µF capacitor?

  • A 2 . 3 × 1 0 C
  • B 1 . 9 × 1 0 C
  • C 5 . 6 × 1 0 C
  • D 1 . 3 × 1 0 C
  • E 2 . 8 × 1 0 C

How much charge is stored by the 15 µF capacitor?

  • A 7 . 8 × 1 0 C
  • B 1 . 9 × 1 0 C
  • C 5 . 9 × 1 0 C
  • D 4 . 3 × 1 0 C
  • E 6 . 8 × 1 0 C

How much charge is stored by the 55 µF capacitor?

  • A 2 . 3 × 1 0 C
  • B 1 . 9 × 1 0 C
  • C 4 . 1 × 1 0 C
  • D 4 . 6 × 1 0 C
  • E 1 . 3 × 1 0 C

How much charge is stored by the 110 µF capacitor?

  • A 5 . 8 × 1 0 C
  • B 1 . 2 × 1 0 C
  • C 4 . 6 × 1 0 C
  • D 3 . 6 × 1 0 C
  • E 1 . 9 × 1 0 C

Q5:

The capacitors in the circuit shown are initially uncharged. When the switch is closed, the capacitors start to charge.

What is the potential difference across the 53 µF capacitor after 45 ms of charging?

What is the potential difference across the 77 µF capacitor after 45 ms of charging?

What is the instantaneous current in the circuit after 45 ms of charging?

Q6:

In a circuit, a capacitor is fully charged and then discharged through a different circuit that contains an uncharged capacitor. The change in the charge stored by each capacitor is shown in the graph. Which of the following statements correctly describes how the capacitances of the two capacitors compare to each other?

  • AThe charging capacitor has the same capacitance as the discharging capacitor.
  • BThe charging capacitor has higher capacitance than the discharging capacitor.
  • CThe discharging capacitor has higher capacitance than the charging capacitor.

Q7:

The capacitors in the circuit shown are initially uncharged. When the switch is closed, the capacitors start to charge.

What is the instantaneous current in the circuit after 75 ms of charging?

  • A 2 . 0 × 1 0 A
  • B 6 . 5 × 1 0 A
  • C 5 . 1 × 1 0 A
  • D 4 . 4 × 1 0 A
  • E 9 . 0 × 1 0 A

What is the potential difference across the 28 µF capacitor after 75 ms of charging?

  • A 7.7 V
  • B 8.4 V
  • C 3.6 V
  • D 2.2 V
  • E 4.5 V

What is the potential difference across the 16 µF capacitor after 75 ms of charging?

  • A 2.8 V
  • B 1.9 V
  • C 4.4 V
  • D 7.6 V
  • E 8.9 V

Q8:

The diagram shows a circuit with a switch that is initially in contact with point 𝐴 . The switch is kept in this position until the 62 µF and 86 µF capacitors are fully charged. The switch is then moved to be in contact with point 𝐵 and the 62 µF and 86 µF capacitors discharge. When the current in the circuit has fallen to zero, some charge is stored in each capacitor.

How much charge is stored in the 44 µF capacitor?

  • A 0 . 7 9 × 1 0 C
  • B 1 . 6 × 1 0 C
  • C 1 . 0 × 1 0 C
  • D 1 . 9 × 1 0 C
  • E 3 . 8 × 1 0 C

How much charge is stored in the 23 µF capacitor?

  • A 1 . 9 × 1 0 C
  • B 1 . 0 × 1 0 C
  • C 1 . 6 × 1 0 C
  • D 3 . 8 × 1 0 C
  • E 0 . 7 9 × 1 0 C

How much charge is stored in the 62 µF capacitor?

  • A 1 . 9 × 1 0 C
  • B 0 . 7 9 × 1 0 C
  • C 1 . 6 × 1 0 C
  • D 1 . 0 × 1 0 C
  • E 3 . 8 × 1 0 C

How much charge is stored in the 86 µF capacitor?

  • A 1 . 0 × 1 0 C
  • B 3 . 8 × 1 0 C
  • C 0 . 7 9 × 1 0 C
  • D 1 . 6 × 1 0 C
  • E 1 . 9 × 1 0 C

Q9:

The diagram shows a circuit with a switch that is initially in contact with the point 𝐴 . The switch is kept in this position until the 15 µF capacitor is fully charged. The switch is then moved to be in contact with the point 𝐵 and the 15 µF capacitor discharges. When the current in the circuit has fallen to zero, some charge is stored in both the 15 µF capacitor and the 25 µF capacitor.

How much charge is stored in the 25 µF capacitor?

  • A 4 . 6 × 1 0 C
  • B 2 . 3 × 1 0 C
  • C 2 . 3 × 1 0 C
  • D 2 . 3 × 1 0 C
  • E 4 . 6 × 1 0 C

How much charge is stored in the 15 µF capacitor?

  • A 4 . 2 × 1 0 C
  • B 2 . 6 × 1 0 C
  • C 7 . 5 × 1 0 C
  • D 1 . 4 × 1 0 C
  • E 3 . 6 × 1 0 C

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