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

An inductor of inductance, $L=400 \mathrm{mH}$ and resistors of resistances $R_1=2 \mathrm{\Omega }$ and $R_2=2 \mathrm{\Omega }$ are connected to a battery of emf $12 \mathrm{V}$as shown in the figure. The internal resistance of the battery is negligible. The switch $S$ is closed at $t=0.$The potential drop across $L$ as a function of time is:

A rectangular loop has a sliding connector $PQ$ of length $l$ and resistance $R \mathrm{\Omega }$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_1, I_2 \mathrm{and} I$ are:

A metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $B$ in the region, the emf induced across the ends of the rod is: