In the circuit shown, when the current '$i$' is $3\text{A}$ and increasing at the rate of $1\text{A/s}$ the measurement of the potential difference between A and B is $12\ \text{V}$. But when the same current $3\text{A}$ is decreasing at the rate of $1\text{A/s}$, the measured potential difference $V_{AB}$ between A and B is $6\text{V}$. The value of 'R' in the circuit is

Two coils have a mutual inductance of $0.005\ \text{H}$. The current changes in the first coil according to equation $I = I_0\sin\omega t$, where $I_0 = 10\ \text{A}$ and $\omega = 60\pi\ \text{rad s}^{-1}$. The maximum values of e.m.f. in the second coil in volt will be

The magnetic potential energy stored in a certain inductor is $49\ \text{mJ}$ when the current in the inductor is $70\ \text{mA}$. The inductance of the inductor is

An a.c. source is applied to a series LR circuit with $X_L = 3R$ and power factor is $X_1$. Now a capacitor with $X_c = R$ is added in series to LR circuit and power factor is $X_2$. The ratio $X_1$ to $X_2$ is