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 the source is changed to ω 3 (but maintaining the same

Question

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 the source is changed to ω 3 (but maintaining the same voltage), then current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency ω .

TestHub · Accepted Answer

At angular frequency ω , the current in R C circuit is given by i r m s = V r m s R 2 + 1 ω C 2 ......(i) A l s o i r m s 2 = V r m s R 2 + 1 ω 3 C 2 = V r m s R 2 + 9 ω 2 C 2 ......(ii) From equation (i) and (ii) we get 3 R 2 = 5 ω 2 C 2 ⇒ 1 ω C R = 3 5 ⇒ X C R = 3 5

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