Capacitor charge and dischargeEdexcel A-Level Physics: Subtopic test

1. 1
   A 2200 μF capacitor is charged to 9.0 V and then discharged through a 47 kΩ resistor.

   (a)

   Which statement defines the time constant of the discharge circuit?

   [1 mark]

   • AThe time for the charge to fall to one tenth of its initial value
   • BThe time for the charge to fall to half of its initial value
   • CThe time taken for the capacitor to discharge completely
   • DThe time for the charge to fall to 1/e of its initial value

   (b)

   Which expression gives the time constant of this circuit?

   [1 mark]

   • ARC
   • BR/C
   • CC/R
   • D1/RC

   (c)

   Calculate the time constant and the potential difference across the capacitor one time constant after discharge begins.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A 470 μF capacitor is charged to 12 V and then discharged through a 10 kΩ resistor. The discharge starts at time t = 0.

   (a)

   What is the current in the resistor at the instant the discharge begins?

   [1 mark]

   • A0.12 mA
   • B1.2 mA
   • C12 mA
   • D4.7 mA

   (b)

   Which statement describes how the current in the resistor varies with time?

   [1 mark]

   • AIt stays constant until the capacitor is empty
   • BIt falls at a constant rate
   • CIt falls exponentially, with the rate of fall proportional to the current at that time
   • DIt rises exponentially

   (c)

   Calculate the current in the resistor 6.0 s after the discharge begins.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A 1000 μF capacitor is charged to 6.0 V and is then discharged through a 22 kΩ resistor.

   (a)

   Calculate how long it takes for the potential difference across the capacitor to fall to 2.0 V.

   [3 marks]

   (b)

   Calculate the charge on the capacitor at that time and the energy dissipated in the resistor up to that time.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student discharges a capacitor of nominal capacitance 2000 μF through an unknown resistor R. A data logger records the potential difference V across the capacitor at regular intervals. She finds that a plot of ln V (with V in volts) against time t in seconds is a straight line with a gradient of −0.050 s⁻¹.

   (a)

   Show that a plot of ln V against t should be a straight line, and use the gradient to determine the resistance R.

   [6 marks]

   (b)

   Describe how the student could obtain reliable data for the discharge of the capacitor, and explain why the voltmeter used must have a very high resistance.

   [6 marks]

   Total for question 4: 12 marks

End of questions