A series – – circuit has

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

Problem

A series

R

–

L

–

C

circuit has

R=20\,\Omega

L=0.10\,\text{H}

and

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

. It is connected to a

120\,\text{V}

(rms) ac source whose frequency can be varied. (i) Derive an expression for the rms current

I

as a function of the angular frequency

\omega

of the supply. (ii) Calculate the resonant frequency

f_{0}

of the circuit and the corresponding maximum current

I_{\max}.

(iii) Determine the two frequencies

f_{1}

and

f_{2}

at which the current falls to

I_{\max}/\sqrt2.

Hence obtain the bandwidth

\Delta f

and the quality factor

Q

of the circuit.