An ac source of angular frequency ω is fed across a resistor R and a capacitor C in series. The current registered is I. if now the frequency of source is changed to ω/3 (but maintain 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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3/5

5/3

2/3

3/2

answer is A.

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Detailed Solution

According to the given problem I=VZ=V[R2+(1/Cω)2]1/2......................(i) And 12=V[R2+(3/Cω)2]1/2...........(ii) Substituting the value of I from equation (i) in (ii), we get4(R2+1C2ω2)=R2+9C2ω2 =1C2ω2=35R2 So that XR=(1/Cω)R=(35R2)1/2R=35

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