An a.c. supply of frequency is applied to a series combination of a resistor ( ) and…

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

Problem

An a.c. supply of frequency

1.0\,\text{kHz}

is applied to a series combination of a resistor (

R=100\,\Omega

) and an inductor (

L=150\,\text{mH}

). A capacitor is now added in series so that the current leads the supply voltage by

30^{\circ}

. (i) Derive the equation relating the required capacitance

C

to the given circuit parameters and solve it to obtain the value of

C

(in

\mu\text{F}

). (ii) Using the value of

C

found in part (i), calculate the magnitude of the impedance of the modified circuit at

1.0\,\text{kHz}

. (iii) If the rms value of the applied voltage is

220\,\text{V}

, find the rms current in the circuit under the above conditions.