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An ac source of angular frequency o is fed across a resistor R and a capacitor C in series. The current registered is l. If now the frequency of source is changed to c/3 (but maintaining the same voltage), the current in the circuit is found to be halved. The ratio of reactance to resistance at the original frequency o will be |
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Answer» `sqrt(3/(5)` and`(1)/(2)=(V)/[[R^(2)+(3)//(Comega^(2))]^(1//2))` Idots(2), substituting the value of Ifrom equation (1) in (2),`4(R^(2)+(1)/(C^(2)omega^(2)))=R^(2)+(9)/(C^(2)omega^(2))`i.e.,`(1)/(C^(2)omega^(2))=(3)/(5)R^(2)` sothat`(X)/(R)=((1//Comega))/(R)=[(3//5)R^(2)]^(1//2)/(R)=sqrt(3)/(5)` |
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