A series circuit containing

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

Problem

R=25\,\Omega

L=50\,\text{mH}

and

C=200\,\mu\text{F}

is connected to a

100\,\text{V}

(rms) ac source whose frequency is variable. The current measured at different frequencies is given below. Frequency

f

(Hz): 50 100 150 200 400 Rms current

I

(A): 1.96 ? 4.00 3.54 ? (i) Calculate the missing current values at

100\,\text{Hz}

and

400\,\text{Hz}.

(ii) Using all five data points, draw a smooth curve of

I

versus

f

on graph paper and mark the approximate resonant frequency. (iii) From your curve, estimate the bandwidth defined between the two frequencies at which the current equals

0.707\,I_{\max}.

(iv) If the resistance is increased to

50\,\Omega

while

L

and

C

remain the same, predict qualitatively how (a) the peak value of current and (b) the width of the resonance curve will change. Justify your answer.

Related theory

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

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