For a series circuit connected to an alternating source of rms voltage and angular…

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

For a series

RLC

circuit connected to an alternating source of rms voltage

V

and angular frequency

\omega

, the rms current is

I

. (i) Derive an expression for the instantaneous power supplied to the circuit in terms of

V

I

and the phase angle

\phi

between them. (ii) By integrating the instantaneous power over one complete cycle, obtain an expression for the average power

P

consumed by the circuit. (iii) Hence deduce the condition under which

P=0

and show that, under this condition, the current either leads or lags the voltage by

90^{\circ}

. (iv) Under the condition obtained in part (iii), write the expression for the rms current in terms of

V

and the effective reactance at that frequency.