A laboratory experiment requires a series LCR circuit to retain the same resonant…

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

Problem

A laboratory experiment requires a series LCR circuit to retain the same resonant frequency while its sharpness of resonance is made four times larger. The initial circuit parameters are

L_{0}=0.25\,\text{H},\;C_{0}=40\,\mu\text{F},\;R_{0}=20\,\Omega

. (i) If the capacitance is reduced to

C=10\,\mu\text{F}

, determine the inductance

L

that will keep the resonant frequency unchanged. (ii) With the new values of

L

and

C

, calculate the resistance

R

that is required so that the quality factor becomes four times the original value. (iii) Compute the ratio of the new bandwidth to the original bandwidth. (iv) Explain briefly, using your numerical results, how simultaneously altering

L

C

and

R

can preserve the tuning of the circuit yet greatly enhance its selectivity.

Related theory

AC Circuit Analysis
Resonance in AC Circuits
Alternating current
Resonance and LC oscillations

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