The mutual induction between primary and secondary coils of a transformer is $2 \mathrm{H}.$. If an $AC$ current of peak value $5 \mathrm{A}$ and frequency $50 \mathrm{Hz}$ flows through the primary coil, then the peak voltage in the secondary coil is, 

A conducting ring of radius a falls vertically downward with a velocity $v_0$ in a horizontal magnetic field $B.$ The potential difference between two points $P$ and $Q$ located symmetrically on both sides of the vertical will be

In the circuit shown in figure, the switch$\text{'}S\text{'}$ is closed at $t=0.$ After closing the switch, (in steady state), the value of current in the resistor $R_3$ as compared to the current through it before closing the switch

There are two stationary coils having mutual inductance $M,$ between them. The current in one of the coils is increasing with time as $I=Kt$ where $K$ is constant and $t$ is the time. The expression for the current in the other coil as a function of time $t,$ its resistance and inductance are $R$ and $L$ respectively is

Three loops $A, B$ and $C,$ and an observer is positioned as shown in the figure. As seen by the observer, constant current $l$ flows in middle loop $B$ in counter-clockwise direction and loop $B$ is moving towards observer with a velocity $v.$ The same observer would notice that

In the circuit shown below, the switch $S$ is closed at $t=0.$ Which of the following best represents the voltage across the inductor?