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Q.

An ac source of angular frequency ω  is fed across a resistor R  and a capacitor C  in series. The current registered isI . If now the frequency of source is changed to ω3 (but maintaining the same voltage), the current in the circuit is found to be halved. Then the ratio of reactance to resistance at the original frequency ω  is

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a

35

b

53

c

23

d

32

answer is A.

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Detailed Solution

According to given problem, I=VZ=V[R2+(1Cω)2]12                   ……..(1)and I2=V[R2+(3Cω)2]12                ……..(2)substituting the value of I from eq.(1) in (2),4(R2+1C2ω2)=R2+9C2ω2 i.e.,1C2ω2=35R2 So that XR=(1Cω)R=(35R2)12R=35 .
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