A series RLC circuit has the following parameters:

PHYSICS · Subjective · CBSE · Physics · Alternating Current · Alternating Current

Problem

R = 10\,\Omega

L = 50\,\text{mH}

and

C = 200\,\mu\text{F}

. It is powered by a 100 V (rms) sinusoidal source. (a) Write the expression for the impedance

Z(\omega)

of the circuit as a function of the angular frequency

\omega

. (b) Show that the current is maximum at the resonant frequency and calculate this maximum rms current. (c) Derive the condition on

\omega

for which the rms current falls to

\dfrac{1}{\sqrt{2}}

times its maximum value. (d) Calculate the two operating frequencies (nearest whole hertz) that satisfy the condition obtained in part (c). (e) State whether these two frequencies lie symmetrically about the resonant frequency and give a brief reason for your observation.

Related theory

Resonance in AC Circuits
AC Circuit Analysis
Series LCR circuit
AC applied to a series LCR circuit
Alternating Current

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