Physics

Problem

A series circuit containing

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. \nFrequency

f

(Hz): 50 100 150 200 400 \nRms 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.

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