Two coils having self-inductance $L_1 = 75$ mH and $L_2 = 48$ mH are coupled with each other. If the mutual inductance of the coils is 37.2 mH, then coefficient of coupling will be

A straight line conductor of length 0.4 m is moved with a speed of $7.0 \text{ ms}^{-1}$ perpendicular to magnetic field of intensity $0.8 \text{ Wb m}^{-2}$. The induced e.m.f. across the conductor is

In LCR circuit, at a particular angular frequency the capacitive reactance and inductive reactance is same. If the angular frequency is doubled, the ratio of the reactance of the capacitor to that of the inductor will be

In an a.c. circuit with pure capacitance 'C' and a.c. source $E = E_0\sin\omega t$, the equation of instantaneous current is given by