Two different coils have self-inductance $3L$ and $L$. The current in both the coils is increased at the same constant rate. At certain instant of time, the power given to the two coils is same. At that time there was current and voltage induced in the two coils. At the same instant, the ratio of energy stored in the first coil to that in the second coil is

Consider two coils in which a current in one coil carrying $6$ A causes the change in the flux in the second coil $12 \times 10^{-4}$ weber/turn. The second coil has $2000$ turns. The mutual inductance between the coils is

Magnetic flux linked with the coil in weber is given by the equation $\Phi = 5t^2 + 6t + 11$. The e.m.f. induced in the coil in the $5^{\text{th}}$ second will be

For a series LCR circuit inductive reactance $X_L$ is equal to resistance $R$ and also equal to twice the capacitive reactance $X_C$. The impedance of the circuit and the phase difference between voltage V and current i are respectively