Charging and discharging capacitorsEdexcel International A Level Physics: Subtopic test

1. 1
   A 2200 μF capacitor is charged to a p.d. of 9.0 V and is then discharged through a 4.7 kΩ resistor.

   (a)

   What is the time constant of this circuit?

   [1 mark]

   • A4.7 × 10⁻⁷ s
   • B10 s
   • C1.0 × 10⁷ s
   • D2.1 × 10⁶ s

   (b)

   Which statement correctly defines the time constant for the discharge of a capacitor through a resistor?

   [1 mark]

   • AThe time for the capacitor to discharge completely
   • BThe time for the charge to fall to half its initial value
   • CThe time for the charge to fall to 63% of its initial value
   • DThe time for the charge to fall to 1/e (about 37%) of its initial value

   (c)

   Calculate the p.d. across the capacitor 20 s after the discharge begins.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A 100 μF capacitor, initially uncharged, is charged through a 47 kΩ resistor using a 6.0 V supply that has negligible internal resistance.

   (a)

   What is the current in the circuit at the instant charging begins?

   [1 mark]

   • A1.3 × 10⁻⁴ A
   • B7.8 × 10³ A
   • C0.13 A
   • D6.4 × 10⁻⁵ A

   (b)

   What is the p.d. across the capacitor one time constant after charging begins?

   [1 mark]

   • A2.2 V
   • B3.0 V
   • C3.8 V
   • D6.0 V

   (c)

   Explain why the current in the circuit decreases as the capacitor charges.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In Core Practical 11 a student records the p.d. V across a capacitor as it discharges through a resistor, using a data logger. She plots ln V against the time t in seconds (V in volts). Her line of best fit is straight, with a gradient of −0.050 s⁻¹ and an intercept of 2.20 on the ln V axis.

   (a)

   Use the equation for exponential discharge to explain the shape of her graph, and determine the time constant of the circuit and the initial p.d. across the capacitor.

   [3 marks]

   (b)

   The resistor in her circuit has a resistance of 100 kΩ. Calculate the capacitance and the time taken for the p.d. to fall to 1.0 V.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student has a 220 μF capacitor, a 47 kΩ resistor, a 6.0 V supply, a two-way switch and a data logger with a voltage sensor. She wants to investigate how the p.d. across the capacitor changes as it discharges and to determine the time constant of the circuit.

   (a)

   Describe how she could use the data logger to find the time constant, including how she would analyse the results.

   [6 marks]

   (b)

   In her experiment the p.d. falls from 6.0 V to 2.2 V in 10 s. Use these readings to determine the time constant and evaluate whether the result agrees with the theoretical value.

   [6 marks]

   Total for question 4: 12 marks

End of questions