PHYSICS · Multi-part · CBSE · Physics · Alternating Current · Alternating Current
Problem
A series circuit consists of a resistor R, an inductor L and a capacitor C connected to an alternating voltage source of angular frequency ω. Answer the following questions about the behaviour of the circuit.
(a) Derive an expression for the impedance Z of the circuit in terms of R, L, C and ω. State clearly any steps involved.
(b) Using the expression obtained in part (a), explain qualitatively how the impedance and hence the current amplitude vary when the driving frequency is (i) much lower than the resonant frequency and (ii) much higher than the resonant frequency.
(c) Identify which of the two reactances (inductive or capacitive) dominates in the frequency ranges mentioned in part (b) and justify your answer without numerical calculation.
(d) Draw a rough, labelled sketch of the variation of current amplitude with angular frequency for the circuit, clearly marking the resonant peak and the regions where the current leads or lags the applied voltage.