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]