A long rectangular conducting loop of width '$l$' mass '$m$' and resistance '$R$' is placed partly in a perpendicular magnetic field '$B$'. With what velocity should it be pushed downwards so that it may continue to fall without any acceleration? ($g$ = acceleration due to gravity)

The following figure represents two bulbs $B_1$ and $B_2$, resistor R and an inductor L. When the switch S is turned off, which of the following statement is true?

An inductor of reactance $100$ $\Omega$, a capacitor of reactance $50$ $\Omega$, and a resistor of resistance $50$ $\Omega$ are connected in series with an AC source of $10$ V, $50$ Hz. Average power dissipated by the circuit is ____

In an AC circuit $E = 50 \sin(500 t)$, $I = 600 \sin\left(500 t + \dfrac{\pi}{3}\right) mA$. What is the power dissipated in the circuit? [$\cos 60^\circ = 0.5$]