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 maintaining the same voltage), the current in then circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency ω
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a
35
b
25
c
15
d
45
answer is A.
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Detailed Solution
At angular frequency ω, the current in RC circuit is given by irms=VrmsR2+1ωC2 ......(i)Also irms2=VrmsR2+1ω3C2=VrmsR2+9ω2C2 ......(ii)From equation (i) and (ii) we get 3R2=5ω2C2⇒1ωCR=35⇒XCR=35