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 $\_\_\_\_$ .

A capacitor C is first charged fully with potential difference of $V_0$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In $t$ s, 25% of the initial energy in the capacitor is transferred to the inductor. The value of $t$ is ________ s.