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.

The dimension of the ratio of magnetic flux and the resistance is equal to that of:

$A$ square coil $ABCD$ lies in the $x-y$ plane with its centre at the origin. $A$ long straight wire passing through the origin carries a current $i = 2t$ in the negative $z$-direction. The induced current in the coil is

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 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: ...... $\mu C$

Radio frequency choke uses a core of