A series RLC circuit is connected to a 200 V (rms) AC source

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

Problem

A series RLC circuit is connected to a 200 V (rms) AC source. The component values are: resistance

R = 20\,\Omega

, inductance

L = 0.10\,\text{H}

and capacitance

C = 100\,\mu\text{F}

. Let the resonant frequency of the circuit be

f_0

. Three operating frequencies are chosen:

f_1 = 0.5f_0

f_0

itself and

f_2 = 2f_0

. (a) Calculate the values of

X_L

and

X_C

at each of the three frequencies. (b) Determine the impedance of the circuit at each frequency. (c) Find the rms current at

f_1

f_0

and

f_2

. (d) Arrange the three current values in ascending order. (e) Identify at which of the three frequencies the circuit behaves inductively and at which it behaves capacitively. Justify your answer in each case.

Related theory

Power in AC Circuits
AC Circuit Analysis
Alternating current
Series LCR circuit
AC applied to a series LCR circuit

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