The network shown in the figure is part of a complete circuit. If at a certain instant,the current $I$ is $5 \ A$ and it is decreasing at a rate of $10^3 \ A \ s^{-1}$,then $V_B - V_A$ equals.....$V$.

$A$ conducting loop in the shape of a right-angled isosceles triangle of height $10 \ cm$ is kept such that the $90^{\circ}$ vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increases at a constant rate of $10 \ As^{-1}$. Which of the following statement$(s)$ is(are) true?
$(A)$ The magnitude of induced emf in the wire is $\left(\frac{\mu_0}{\pi}\right) \ V$
$(B)$ If the loop is rotated at a constant angular speed about the wire,an additional emf of $\left(\frac{\mu_0}{\pi}\right) \ V$ is induced in the wire
$(C)$ The induced current in the wire is in the opposite direction to the current along the hypotenuse
$(D)$ There is a repulsive force between the wire and the loop

In an $L-R$ circuit connected to a battery,the rate at which energy is stored in the inductor is plotted against time during the growth of the current in the circuit. Which of the following best represents the resulting curve?

$A$ coil of self-inductance $L$ is connected at one end of two rails as shown in the figure. $A$ connector of length $l$ and mass $m$ can slide freely over the two parallel rails. The entire setup is placed in a magnetic field of induction $B$ directed into the page. At an instant $t = 0$,an initial velocity $v_0$ is imparted to the connector,and as a result,it starts moving along the $x$-axis. Which of the following graphs best represents the displacement $x$ of the connector as a function of time $t$?

$AB$ is a part of an electrical circuit (see figure). The potential difference $V_{A}-V_{B}$, at the instant when current $i=2 \text{ A}$ and is increasing at a rate of $1 \text{ A/s}$, is: (in $\text{ V}$)

$A$ small circular loop of area $A$ and resistance $R$ is fixed on a horizontal $xy$-plane with the center of the loop always on the axis $\hat{n}$ of a long solenoid. The solenoid has $m$ turns per unit length and carries current $I$ counterclockwise as shown in the figure. The magnetic field due to the solenoid is in $\hat{n}$ direction. $List-I$ gives time dependences of $\hat{n}$ in terms of a constant angular frequency $\omega$. $List-II$ gives the torques experienced by the circular loop at time $t=\frac{\pi}{6\omega}$. Let $\alpha=\frac{A^2 \mu_0^2 m^2 I^2 \omega}{2R}$.

$List-I$	$List-II$
$(I)$ $\frac{1}{\sqrt{2}}(\sin \omega t \hat{j}+\cos \omega t \hat{k})$	$(P)$ $0$
$(II)$ $\frac{1}{\sqrt{2}}(\sin \omega t \hat{i}+\cos \omega t \hat{j})$	$(Q)$ $-\frac{\alpha}{4} \hat{i}$
$(III)$ $\frac{1}{\sqrt{2}}(\sin \omega t \hat{i}+\cos \omega t \hat{k})$	$(R)$ $\frac{3\alpha}{4} \hat{i}$
$(IV)$ $\frac{1}{\sqrt{2}}(\cos \omega t \hat{j}+\sin \omega t \hat{k})$	$(S)$ $\frac{\alpha}{4} \hat{j}$

Which one of the following options is correct?