A coil of inductance $L$ has an inductive reactance of ${X_L}$ in an AC circuit in which the effective current is I. The coil is made from a super-conducting material and has no resistance. The rate at which power is dissipated in the coil is

An inductor $(L = 100\ mH)$, a resistor $(R = 100 \Omega)$ and a battery $(E = 100\ V)$ are initially connected in series as shown in the figure. After a long time the battery is disconnected after short circuiting the points $A $ and $ B$. The current in the circuit $1\ ms$ after the short circuit is

An $a.c.$ source of voltage $V$ and of frequency $50\,Hz$ is connected to an inductor of $2H$ and negligible resistance. $A$ current of $r.m.s.$ value $I$ flows in the coil. When the frequency of the voltage is changed to $400\,Hz$ keeping the magnitude of $V$ the same, the current is now

Two resistors of $10\, \Omega$ and $20\, \Omega$ and an ideal inductor of $10\, H$ are connected to a $2\, V$ battery as shown. The key $K$ is inserted at time $t = 0$. The initial $(t = 0)$ and final ($t \rightarrow \infty$ ) currents through battery are

For the circuit shown in the fig., the current through the inductor is $0.9\,A$ while the current through the condenser is $0.4\,A$. Then