16P. Capacitors (2026) NJC tutorial

National Junior College Science Department | Physics 1 16. Capacitors Problem set Formulae capacitors in series 1C = 1C1 + 1C2 +⋯ capacitors in parallel C=C1+C2+⋯ energy in a capacitor U= 12 QV= 12Q2C = 12 CV2 charging a capacitor Q=Q0%1−e!t!' discharging a capacitor Q=Q0e!t! RC time constant (= RC (Suggested duration: 120 minutes) 1 (a) Two flat metal plates are held by a small distance apparat by means of insulating pads. Explain how the plates could act as a capacitor. [2] (b) An initially uncharged capacitor X, of capacitance C, is gradually charged by a power supply so that the final potential difference (p.d.) between its plates is V and the final charge is Q. (i) Sketch the variation of charge with p.d. for capacitor X as the p.d. increases from 0 to V. [2] (ii) Determine an expression, in terms of Q and V, for the work W done on capacitor X during the charging process. Explain your reasoning. [2]

National Junior College Science Department | Physics 2 (c) The charged capacitor in (b) is now disconnected from the supply. The plates of the capacitor are initially separated by distance L. They are then moved closer together by a distance D as shown. (i) By considering the electric field between the plates, show that the new p.d. VN between the plates is given by: VN=)L−DL*V Explain your reasoning. [2] (ii) Deduce the expression for the new capacitance CN in terms of C, L and D. Explain your reasoning. [3] 2 (a) A student has available four capacitors, each of capacitance 24 µF. The capacitors are connected as shown. Calculate the combined capacitance between the terminals X and Y. [2] (b) A student has available three capacitors, each of capacitance 12 µF. Draw diagrams, one in each case, to show how the student connects the capacitors to give a combined capacitance between the terminals of: (i) 18 µF, [1] (ii) 8 µF. [1]

National Junior College Science Department | Physics 3 3 (a) Two parallel plate capacitors C1 and C2 are connected to a supply that has a potential difference (p.d.) VS. The capacitors may be connected in series or in parallel. The supply provides charge QS and the plates of the two capacitors acquire charges Q1 and Q2 respectively. The p.d.s across the plates of the capacitors are V1 and V2 respectively. Complete the table below to indicate how QS, Q1 and Q2 relate to each other, and how VS, V1 and V2 relate to each other, for series and parallel connections of the capacitors to the supply. relationship between charges relationship between p.d.s series parallel [4] (b) Two capacitors A and B are connected into the circuit shown below. Capacitor A has capacitance 470 µF and capacitor B has capacitance 180 µF. The two-way switch S is initially at position X, and capacitor B is initially uncharged. Capacitor A stores 19 mJ of energy when fully charge. (i) Calculate the e.m.f. of the cell. [2] (ii) Calculate the charge on the capacitor A. [2] (iii) The two-way switch S is now moved to position Y. Determine 1. the final p.d. across capacitor B, [3] 2. the decrease in the total energy, in mJ, stored in the two capacitors. [2]

National Junior College Science Department | Physics 4 4 Two capacitors of capacitances 22 µF and 47 µF, and a resistance of 2.7 MΩ, are connected into the circuit as shown. The battery has an e.m.f. of 12 V. The two-way switch S is initially at position X, so that the capacitors are fully charged. The two-way switch is then moved to position Y. Determine the time taken for the p.d. across the 22 µF capacitor to become 6.0 V. [4]

National Junior College Science Department | Physics 5 5 A capacitor of capacitance C and a resistor of resistance R are connected, as shown in Fig. (a). Fig. (a) Initially, the capacitor is charged and the switch is open. The switch is closed at time t = 0. Fig. (b) and Fig. (c) show, respectively, the variations with t of the charge Q on the capacitor and the potential difference (p.d.) V across the resistor. Fig. (b) Fig. (c) (a) Explain the shape of the line in Fig. (c) representing the variation of V with t. [3] (b) Use Fig. (b) to show that the time constant of the circuit in Fig. (a) is 5.5 s. [3] (c) Using Fig. (b), Fig. (c) and the information in (b) to determine: (i) capacitance C, in µF, [2] (ii) resistance R, in kΩ. [2]

National Junior College Science Department | Physics 6 6 Fig. (a) shows a circuit contains a capacitor of capacitance C and a resistor of resistance R. Fig. (a) Initially, the switch is open and the p.d. across the capacitor is 12 V. The switch is closed at time t = 0 and the capacitor discharges through the resistor. Fig. (b) shows the variation of the charge Q on the capacitor with the p.d. VC across the capacitor as the capacitor discharges. Fig. (c) shows the variation of the current I in the resistor with the p.d. VR across the resistor as the capacitor discharges. Fig. (b) Fig. (c) Use Fig. (b) and Fig. (c) to (a) explain why the variation of Q with t is exponential in nature. [3] (b) determine the time constant of the circuit. [3]

National Junior College Science Department | Physics 7 7 The circuit in Fig. (a) produces half-wave rectification of an alternating input voltage VIN to produce output voltage VOUT across the resistor R. Fig. (a) The input voltage VIN is a square wave. Fig. (b) shows the variation of VIN with time t. Fig. (b) Fig. (c) shows the variation of the output voltage VOUT with t. Fig. (c) The maximum energy stored in the capacitor is 0.041 J. (a) State the purpose of the capacitor C in the circuit. [1] (b) Show that the capacitance of C is 570 µF. [1] (c) Determine the resistance of R. [3]

National Junior College Science Department | Physics 8 Challenging questions C1 Three capacitors are arranged as shown. Determine the effective capacitance between X and Y. C2 A capacitor made from two thin, flat metal sheets separated by a small thickness of insulating material has a capacitance C. Each metal sheet is then cut into four smaller identical sheets, which are used to make another capacitor as shown. The same thickness of insulator is used between the interleaved sheets. Neglecting end-effects, determine the capacitance of the reconstructed capacitor. C3 A circuit containing a capacitor of fixed capacitance C and a variable capacitor. The e.m.f. of the battery is ,". Initially, with the switch closed, the variable capacitor is set so as to have a capacitance of exactly C. The switch is then opened. Finally, with the switch still open, the variable capacitor is adjusted to have a capacitance of fC, where f is less than 1. (a) Show that the resulting potential difference ,# across the fixed capacitor is given by ,#=2,"1+/ and determine the potential difference across the variable capacitor. (b) Show that the total energy stored in the capacitors after the final adjustment is more than the initial total energy, and find an expression for the energy difference. Give your answer in terms of f, C and ,". Explain how you can reconcile this result with the principle of conservation of energy.

National Junior College Science Department | Physics 9 C4 In the circuit shown, all three switches S1, S2 and S3 are initially open. The battery has an e.m.f. V0 with no internal resistance. The capacitors C1 and C2 are ideal. The connecting wires have zero resistance. (a) While switches S2 and S3 are open, state the expression for the energy E stored in the capacitor C1 in terms of V0, R and C1. [1] (b) After a long time, the capacitor C1 becomes fully charged. Switch S1 is then opened. (i) On closing switch S2, while S1 and S3 remain open, it is noticed that a spark develops between the contacts of the switch. By considering the change in ener