A variable capacitor is connected in series with a fixed inductor to form a…

PHYSICS · Multi-part · CBSE · Physics · Alternating Current · Alternating Current

Problem

A variable capacitor is connected in series with a fixed inductor to form a radio–frequency tuning circuit. (i) Starting from the condition for resonance in a series

LCR

circuit, derive an expression for the resonant frequency

f_0

in terms of the inductance

L

and capacitance

C

. (ii) For a fixed inductance of

1.0\,\text{mH}

, the capacitance is varied from

100\,\text{pF}

400\,\text{pF}

. Calculate the percentage change in the resonant frequency resulting from this adjustment. (iii) A different set-up uses an inductance of

0.20\,\text{mH}

to tune radio broadcasts between

700\,\text{kHz}

and

1400\,\text{kHz}

. Determine the range over which the capacitance must be varied to cover this entire frequency band.

Related theory

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

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