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

An alternating voltage $e = 150\sqrt{2}\sin 100t$ volt is applied to a capacitor of capacity $2\ \mu\text{F}$. The root mean square value of current in the circuit is