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

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 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

Infinity Learn · Accepted Answer

At angular frequency ω, the current in RC circuit is given by $$irms=VrmsR2+1$$ω$$C2$$    ......(i)Also$$ $$irms2=VrmsR2+1$$ω$$3C2=VrmsR2+9$$ω$$2C2$$      ......$$(ii)From$$ equation $$(i) and (ii) we get $$3R2=5$$ω$$2C2$$⇒$$1$$ω$$CR=35$$⇒$$XCR=35$$

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