Two identical coaxial circular loops carry a current $i$ each,circulating in the same direction. If the loops approach each other,then:

As per the given figure,if $\frac{ dI }{ dt } = -1 \text{ A/s}$,then the value of $V_{AB}$ at this instant will be $.......... \text{ V}$.

The current $i$ in an inductance coil varies with time $t$ according to the following graph. Which one of the following plots shows the variations of voltage $V$ in the coil?

$A$ metallic square wire loop of side $10\, cm$ and resistance $1\,\Omega$ is moved with a constant velocity $v_0$ in a uniform magnetic field of induction $B = 2\, T$ as shown in the figure. The magnetic field is perpendicular into the plane of the loop. The loop is connected to a network of resistors each of value $3\,\Omega$. The resistance of the lead wires $OS$ and $PQ$ are negligible. What should be the speed of the loop so as to have a steady current of $1\, mA$ in it? Give the direction of current in the loop.

Two metallic rings $A$ and $B$,identical in shape and size but having different resistivities $\rho_A$ and $\rho_B$,are kept on top of two identical solenoids as shown in the figure. When current $I$ is switched on in both the solenoids in an identical manner,the rings $A$ and $B$ jump to heights $h_A$ and $h_B$,respectively,with $h_A > h_B$. The possible relation$(s)$ between their resistivities and their masses $m_A$ and $m_B$ is(are):
$(A)$ $\rho_A > \rho_B$ and $m_A = m_B$
$(B)$ $\rho_A < \rho_B$ and $m_A = m_B$
$(C)$ $\rho_A > \rho_B$ and $m_A > m_B$
$(D)$ $\rho_A < \rho_B$ and $m_A < m_B$

The figure shown has two coils of wires placed in close proximity. The current in primary coil $P$ is made to vary with time as shown in the graph. Which of the following graphs best represents the variation of the emf induced in the secondary coil $S$?