7.3.2 Charge and discharge of resistor-capacitor circuits Quiz: Pearson Edexcel Physics, Unit 7

The 20 questions

1. What are the units of the time constant RC of a resistor-capacitor circuit?

   • Ohms
   • Volts per second
   • Seconds
   • Farads

2. What percentage of initial charge remains on a discharging capacitor after one time constant?

   • 50%
   • 5%
   • 63%
   • 37%

3. For the discharge Q = Q0 e^(-t/RC), what is the gradient of a graph of ln Q against t?

   • -RC
   • -1/Q0
   • RC / Q0
   • -1/RC

4. How does current vary with time during the discharge of a capacitor through a resistor?

   • Linear decrease
   • Exponential decrease
   • Constant value
   • Exponential increase

5. How long does it take for a discharging capacitor's charge to fall to 1/e of its original value?

   • Half a second
   • Two time constants
   • e seconds
   • One time constant

6. A 2.0 megohm resistor is connected in series with a 4.0 microfarad capacitor. What is the time constant?

   • 8.0 s
   • 0.50 s
   • 2.0 s
   • 8.0 x 10^-12 s

7. A 100 microfarad capacitor charged to 12 V discharges through a 10 kilohm resistor. What is the potential difference across it after 1.0 s?

   • 6.0 V
   • 0.44 V
   • 4.4 V
   • 8.0 V

8. Using the same circuit, how long does the potential difference take to fall to half its initial value?

   • 1.4 s
   • 0.50 s
   • 1.0 s
   • 0.69 s

9. A capacitor with initial charge 2.0 millicoulomb has a time constant of 0.50 s. What is the charge on it after 0.50 s of discharge?

   • 1.0 mC
   • 0.27 mC
   • 0.14 mC
   • 0.74 mC

10. A 12 V supply charges and then discharges through a 10 kilohm resistor and a 100 microfarad capacitor. What is the current at t = 1.0 s during discharge, given the initial current is 1.2 mA?

    • 4.4 mA
    • 0.44 mA
    • 0.12 mA
    • 1.2 mA

11. A capacitor charged to 9.0 V discharges through a resistor with time constant 2.0 s. What is the potential difference after 4.0 s?

    • 3.3 V
    • 4.5 V
    • 0.45 V
    • 1.2 V

12. A capacitor is charged through a 1.0 kilohm resistor from a 10 V supply. What is the potential difference across the capacitor after one time constant of 1.0 s?

    • 10 V
    • 8.6 V
    • 3.7 V
    • 6.3 V

13. Which change will increase the time constant of a resistor-capacitor discharge circuit?

    • Decreasing capacitance
    • Increasing capacitance
    • Decreasing resistance
    • Increasing supply voltage

14. A graph of ln V against t for a discharging capacitor is a straight line with gradient -0.20 s^-1. What is the time constant?

    • 5.0 s
    • 0.80 s
    • 0.20 s
    • 2.0 s

15. A capacitor starts discharging from 6.0 V. What is its potential difference after three time constants?

    • 2.0 V
    • 0.03 V
    • 0.30 V
    • 0.60 V

16. A 2.0 kilohm resistor is in series with a 1000 microfarad capacitor being charged from a 10 V supply. How long does the capacitor take to reach 90 per cent of the supply voltage?

    • 0.90 s
    • 6.9 s
    • 4.6 s
    • 2.0 s

17. A capacitor with time constant 0.80 s discharges through a resistor. How long does its stored energy take to fall to one quarter of its initial value?

    • 0.55 s
    • 0.40 s
    • 0.20 s
    • 1.6 s

18. On a graph of ln V against t, a discharging capacitor's line passes through ln V = 2.30 at t = 0 and ln V = 0.00 at t = 10 s. What is the time constant RC?

    • 10 s
    • 4.3 s
    • 2.3 s
    • 0.23 s

19. Why is the discharge current of a capacitor greatest at the start of discharge?

    • Charge is zero
    • Capacitance is maximum
    • Resistance is lowest
    • Initial p.d. is maximum

20. Why does a discharging capacitor never theoretically reach zero charge?

    • Resistance drops to zero
    • It decays asymptotically
    • It decays linearly
    • Voltage remains constant

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