A full set of ten original structured questions in the style of Paper 4, covering the whole of Capacitance: capacitance and combinations, the energy stored, and exponential discharge. Several questions chain capacitance into the stored energy and on into discharge, all within the topic. Each is linked to its lessons; attempt them all, then reveal the worked solutions.
A capacitor C₁ = 100 µF is charged to a potential difference of 12 V. A second capacitor C₂ = 200 µF is then connected to it, either in parallel or in series, as shown in Fig. 1.1.
(a) Define capacitance and state its unit. [2]
(b) Calculate the charge stored on C₁ alone at 12 V. [2]
(c) Calculate the combined capacitance when C₁ and C₂ are connected in parallel. [1]
(d) Calculate the total charge stored by the parallel combination at 12 V. [2]
(e) Calculate the combined capacitance when the two are connected in series. [2]
(f) Explain why the series combination has a smaller capacitance than either capacitor alone. [2]
(g) State how the charge on each capacitor compares in the series arrangement. [1]
(h) State the unit of capacitance in base form. [1]
A 2200 µF capacitor is charged to a potential difference of 9.0 V. Fig. 2.1 shows how the voltage across a capacitor varies with the charge stored.
(a) Calculate the charge stored on the capacitor. [2]
(b) Calculate the energy stored, using W = ½CV². [2]
(c) Show that this is equal to ½QV. [2]
(d) The capacitor is instead charged to 18 V. State and explain the new energy stored. [2]
(e) Using Fig. 2.1, explain why the energy is ½QV and not QV. [2]
(f) The capacitor is then fully discharged through a resistor. State what happens to the stored energy. [2]
(g) Write a third expression for the energy in terms of Q and C. [1]
A 470 µF capacitor is charged to 6.0 V and then discharged through a 10 kΩ resistor. Fig. 3.1 shows how the voltage across the capacitor falls with time.
(a) Calculate the time constant of the circuit. [2]
(b) Write down the equation giving the voltage at time t. [1]
(c) Calculate the voltage across the capacitor after one time constant. [2]
(d) Calculate the time taken for the voltage to fall to 1.5 V. [3]
(e) State and explain the effect on the time constant of doubling the resistance. [2]
(f) Describe how the discharge current varies with time. [2]
A capacitor stores a charge of 6.0 μC when the potential difference across it is 3.0 V.
(a) Define capacitance. [2]
(b) Calculate the capacitance. [2]
(c) State the unit of capacitance and express it in terms of the coulomb and the volt. [1]
(d) Calculate the charge stored when the p.d. is raised to 8.0 V. [2]
(e) State and explain how the stored charge changes if the p.d. is doubled. [2]
(f) State what is stored on the two plates of a charged capacitor. [1]
Three capacitors of 2.0 μF, 3.0 μF and 6.0 μF are available.
(a) Calculate the total capacitance when they are connected in parallel. [2]
(b) Calculate the total capacitance when they are connected in series. [3]
(c) State how the charge on each capacitor compares when they are in series. [1]
(d) State how the p.d. across each compares when they are in parallel. [1]
(e) The parallel combination is connected to a 12 V supply. Calculate the total charge stored. [2]
(f) For the series combination across 12 V, calculate the charge on each capacitor. [2]
A 4.7 μF capacitor is charged to 9.0 V. Parts (a) and (b) use capacitance; the rest use the energy stored.
(a) Calculate the charge stored. [2]
(b) State what happens to the charge if the capacitor is disconnected from the supply. [1]
(c) Calculate the energy stored. [2]
(d) Calculate the energy stored if the voltage were doubled to 18 V. [2]
(e) State and explain the factor by which the stored energy increases when the voltage is doubled. [3]
Fig. 7.1 shows how the charge on a capacitor varies with the p.d. across it.
(a) Write three equivalent expressions for the energy stored in a capacitor. [2]
(b) Explain, with reference to the Q-V graph, why the energy is ½QV and not QV. [3]
(c) A 100 μF capacitor is charged to 50 V. Calculate the energy stored. [2]
(d) Calculate the charge stored. [2]
(e) The capacitor is discharged through a flash lamp in 2.0 ms. Calculate the average power delivered. [2]
A 10 μF capacitor charged to 12 V is connected across an uncharged 5.0 μF capacitor. This question links capacitance with the stored energy.
(a) Calculate the initial charge on the 10 μF capacitor. [2]
(b) After connection the charge is shared. Calculate the common p.d. across the two capacitors. [3]
(c) Calculate the total energy stored before and after the connection. [3]
(d) Calculate the energy that appears to be lost, and state where it goes. [2]
(e) State why the charge is conserved but the energy is not. [1]
A 220 μF capacitor charged to 10 V discharges through a 47 kΩ resistor, as in Fig. 9.1.
(a) Write the equation for the charge on the capacitor during the discharge. [1]
(b) Calculate the time constant. [2]
(c) State the physical meaning of the time constant. [2]
(d) Calculate the p.d. across the capacitor after 5.0 s. [3]
(e) Calculate the time for the p.d. to fall to 2.0 V. [3]
A 470 μF capacitor is charged to 6.0 V and then discharged through a 10 kΩ resistor. This question uses all three lessons of the topic: capacitance, energy, and discharge.
(a) Calculate the initial charge stored. [2]
(b) Calculate the initial energy stored. [2]
(c) Calculate the time constant of the discharge. [2]
(d) Calculate the p.d. across the capacitor after 3.0 s. [3]
(e) Calculate the energy still stored at that time. [3]
Mark this once you have attempted all ten questions and checked your working against the solutions. Revealing the solutions alone does not count.