NYJC_EJC 2026 RLC Circuits (Oscillatory) Tutorial

Page 1 of 6 9814 (202 6) H3 Physics H305 Capacitors and Inductors (Oscillatory) – Tutorial H3 Physics Topic 5 - Capacitors and Inductors (Oscillatory) 11 A series circuit consists of a capacitor of capacitance C, an inductor of inductance L and a switch, as shown in Fig. 11.1. Fig. 11.1 Initially, the switch is open and the capacitor holds a charge Qo. (a) Compare how the energy is stored in a capacitor and in an inductor. C L

Page 2 of 6 9814 (202 6) H3 Physics H305 Capacitors and Inductors (Oscillatory) – Tutorial (b) The switch is closed at time t = 0 and the capacitor begins to discharge through the inductor. Show that the charge q on the capacitor obeys the equation 2 2 1 0dq q dt LC += .

Page 3 of 6 9814 (202 6) H3 Physics H305 Capacitors and Inductors (Oscillatory) – Tutorial (c) (i) Deduce an expression for the natural frequency fo of the circuit. (ii) Determine an expression for the charge q as a function of time, q(t). (iii) On Fig. 11.2, draw two separate graphs to show the variation with time of the charge q on the capacitor and the current I in the circuit. Fig. 11.2 0 time

Page 4 of 6 9814 (202 6) H3 Physics H305 Capacitors and Inductors (Oscillatory) – Tutorial (iv) Show that the total energy ET of the circuit for t > 0 is given by the expression 2 2 o T QE C = (d) A resistor of resistance R is now added in series with the capacitor and inductor as shown in Fig. 9.3. Fig. 11.1 The capacitor is again fully charged and the switch is closed at time t = 0. The charge q on the capacitor obeys the equation 2 2 1 0dq q dt LC R dq L dt += + Assuming that 2 LR C << , an expression of the form ( )cos t oq Qe t γ ωϕ − = + is a general solution of this equation. C L R

Page 5 of 6 9814 (202 6) H3 Physics H305 Capacitors and Inductors (Oscillatory) – Tutorial (i) Determine the expressions for the constants γ in terms of R and L, and ω in terms of γ and ωo where 2oo fωπ= and fo is the natural frequency of the circuit in (c)(i).

Page 6 of 6 9814 (202 6) H3 Physics H305 Capacitors and Inductors (Oscillatory) – Tutorial (ii) Derive an expression for the half -life time τ of the circuit, when the energy of the system drops to half of its initial value.

Page 1 of 7 9814 (202 6) H3 Physics H305 Capacitors and Inductors (Oscillatory) – Tutorial Solutions H3 Physics Topic 5 - Capacitors and Inductors (Oscillatory) Name: ____________________________________________ Class: ______________ 11 A series circuit consists of a capacitor of capacitance C, an inductor of inductance L and a switch, as shown in Fig. 11.1. Fig. 11.1 Initially, the switch is open and the capacitor holds a charge Qo. (a) Compare how the energy is stored in a capacitor and in an inductor. C L In a capacitor, the energy is stored in the electric