Capacitor charge and dischargeAQA A-Level Physics: Subtopic test

1. 1
   A 1000 µF capacitor is charged to 6.0 V and then discharged through a 22 kΩ resistor.

   (a)

   What is the time constant of the circuit?

   [1 mark]

   • A22 s
   • B2.2 × 10⁷ s
   • C2.2 × 10⁻² s
   • D15 s

   (b)

   How long does it take for the p.d. across the capacitor to fall to 3.0 V?

   [1 mark]

   • A22 s
   • B32 s
   • C15 s
   • D7.6 s

   (c)

   The 22 kΩ resistor is replaced by a 44 kΩ resistor. State and explain the effect on the initial discharge current and on the time taken for the capacitor to discharge.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A 470 µF capacitor charged to 9.0 V is discharged through a 10 kΩ resistor.

   (a)

   What is the p.d. across the capacitor 4.7 s after the discharge begins?

   [1 mark]

   • A4.5 V
   • B5.7 V
   • C1.2 V
   • D3.3 V

   (b)

   What is the p.d. across the capacitor 10 s after the discharge begins?

   [1 mark]

   • A7.9 V
   • B1.1 V
   • C4.1 × 10⁻⁴ V
   • D5.6 V

   (c)

   Calculate the discharge current at the start and 4.7 s later.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A 1500 µF capacitor, initially uncharged, is connected in series with a 3.3 kΩ resistor to a 12 V supply of negligible internal resistance, so that it charges through the resistor.

   (a)

   Calculate the p.d. across the capacitor 6.0 s after the circuit is connected.

   [3 marks]

   (b)

   Calculate the time taken for the capacitor to reach 90% of its final p.d., and the current in the circuit at that instant.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In a required practical, a student discharges a capacitor through a 47 kΩ resistor and uses a stopwatch to time p.d. readings every 10 s from a digital voltmeter of resistance 10 MΩ connected across the capacitor. She plots a graph of ln V against t (V in volts, t in seconds) and obtains a straight line with a gradient of −0.050 s⁻¹ and an intercept of 2.20 on the ln V axis.

   (a)

   Explain why a graph of ln V against t is a straight line, and use the student's graph to determine the capacitance and the initial p.d. across the capacitor.

   [6 marks]

   (b)

   Calculate the time for the p.d. to halve, using the student's data. Evaluate two features of the method that make the value of the time constant reliable.

   [6 marks]

   Total for question 4: 12 marks

End of questions