A resistor of and an inductor of are connected in series with a variable capacitor to…

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

Problem

A resistor of

20\,\Omega

and an inductor of

150\,\text{mH}

are connected in series with a variable capacitor to an AC source of fixed frequency

1.0\,\text{kHz}

and r.m.s. voltage

100\,\text{V}

. The value of the capacitor is adjusted until the current is observed to lead the source voltage by

45^{\circ}

. (i) Starting from the general expression for the phase angle, obtain a formula for the capacitance

C

required to make the current lead the voltage by

45^{\circ}

at the given frequency. (ii) Calculate the numerical value of this capacitance (in

\mu\text{F}

, correct to two significant figures). (iii) For the capacitance found in part (ii), compute the impedance of the circuit and hence determine the r.m.s. current drawn from the source.

Related theory

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

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