question_answer

An ac source of angular frequency \[\omega \] 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 \[\omega /3\] (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\[\omega \].

Answer:

\[\left( \sqrt{\frac{3}{5}} \right)\]