The expression for the magnetic energy stored in a solenoid of length $L$, in terms of magnetic field $B$ and area $A$ is

An aeroplane is travelling horizontally towards west with a speed of $540 \mathrm{kmh}^{-1}$. The wing span of the plane is 20 m . If the horizontal component of the earth's magnetic field at the location is $2.5 \sqrt{3} \times 10^{-4} \mathrm{~T}$ and the dip angle is $30^{\circ}$, the potential difference developed between the ends of the wing is

A series $L-C-R$ circuit is connected to an AC source of voltage $150 \sin (80 \pi t)$ volt. If the resistance of the resistor in the circuit is $25 \Omega$ and the impedance in the circuit is $75 \Omega$, the average power dissipated per cycle in the circuit is

The displacement current through the plates of a parallel plate capacitor of capacitance $30 \mu \mathrm{~F}$ is $150 \mu \mathrm{~A}$. The capacitor is charged by a source of varying potential at the rate of