An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega / 4$, (keeping the voltage unchanged) the current is found to be $I / 3$. The ratio of resistance to reactance at frequency $\omega$ is

The figure given below shows an LCR series circuit with two switches S₁ and S₂. When switch S₁ is closed keeping S₂ open, the phase difference (φ) between the current and source voltage is 30° and phase difference is 60° when S₂ is closed keeping S₁ open. The value of (3L₁ − L₂) is ______ H.

The electric current in the circuit is given as $i=i_{\mathrm{o}}(t / T)$. The r.m.s current for the period $t=0$ to $t=T$ is $\_\_\_\_$ .

For the series LCR circuit connected with $220 \mathrm{~V}, 50 \mathrm{~Hz}$ a.c source as shown in the figure, the power factor is $\frac{\alpha}{10}$. The value of $\alpha$ is $\_\_\_\_$ .