The diagram below shows two coils $A$ and $B$ placed parallel to each other at a very small distance. Coil $A$ is connected to an ac supply. $G$ is a very sensitive galvanometer. When the key $K$ is closed:

$A$ conducting loop of finite resistance lies on the $x-y$ plane. There is a constant magnetic field in the $z$ direction. The area of the loop varies with time $t$, as $A = A_0 (1 + \sin t)$ in appropriate units. The figure that correctly indicates the qualitative behaviour of the power $P$ dissipated in the loop as a function of time is :

$A$ conducting square loop initially lies in the $XZ$ plane with its lower edge hinged along the $X$-axis. Only in the region $y \geq 0$,there is a time-dependent magnetic field pointing along the $Z$-direction,$\vec{B}(t) = B_0(\cos \omega t) \hat{k}$,where $B_0$ is a constant. The magnetic field is zero everywhere else. At time $t=0$,the loop starts rotating with constant angular speed $\omega$ about the $X$-axis in the clockwise direction as viewed from the $+X$ axis (as shown in the figure). Ignoring self-inductance of the loop and gravity,which of the following plots correctly represents the induced e.m.f. $(V)$ in the loop as a function of time?

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

Match the List-$I$ with List-$II$:

List-$I$	List-$II$
$A$. Magnetic induction	$I$. $MLT^{-2}A^{-2}$
$B$. Magnetic flux	$II$. $ML^2T^{-2}A^{-2}$
$C$. Magnetic permeability	$III$. $ML^0T^{-2}A^{-1}$
$D$. Self inductance	$IV$. $ML^2T^{-2}A^{-1}$

Choose the correct answer from the options given below:

The current in the given circuit is increasing at a rate of $\frac{dI}{dt} = 4 \, A/s$. The charge on the capacitor at an instant when the current in the circuit is $2 \, A$ will be: ...... $\mu C$