Resistor of resistance R and capacitor of capacitance C are connected in series to an AC source of angular frequency `omega` . Rms current in the circuit is I. When frequency of the source is changed to one - third of initial value keeping the voltage same then current is found to be halved. Find the ratio of reactance of capacitor to that with resistance at the original frequency `omega` .

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the initial conditions
We have a resistor of resistance \( R \) and a capacitor of capacitance \( C \) connected in series to an AC source with angular frequency \( \omega \). The RMS current in the circuit is \( I \).

### Step 2: Write the expression for impedance
The impedance \( Z \) of the series circuit is given by:
\[
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