The current $I$ through a coil varies with time $t$ as shown in the graph. Plot the graph for the induced $emf$ $e$ versus time $t$ for the coil.

$A$ circular insulated copper wire loop is twisted to form two loops of area $A$ and $2A$ as shown in the figure. At the point of crossing,the wires remain electrically insulated from each other. The entire loop lies in the plane of the paper. $A$ uniform magnetic field $\vec{B}$ points into the plane of the paper. At $t=0$,the loop starts rotating about the common diameter as an axis with a constant angular velocity $\omega$ in the magnetic field. Which of the following options is/are correct?
[$A$] The rate of change of the flux is maximum when the plane of the loops is perpendicular to the plane of the paper.
[$B$] The net emf induced due to both the loops is proportional to $\cos \omega t$.
[$C$] The emf induced in the loop is proportional to the sum of the areas of the two loops.
[$D$] The amplitude of the maximum net emf induced due to both the loops is equal to the amplitude of maximum emf induced in the smaller loop alone.

Which of the following is constructed on the principle of electromagnetic induction?

The current $i$ in a coil varies with time as shown in the figure. The variation of induced $emf$ with time would be

$A$ current $I = 10 \ A$ is passed through the part of a circuit shown in the figure. What will be the potential difference between $A$ and $B$ when $I$ is decreased at a constant rate of $10^2 \ A \ s^{-1}$ (in $V$)?

The current through a coil varies according to the following graph. Plot the graph for induced $emf$ $(e)$ versus time $(t)$ for the coil.