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.....$V$.

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 $m_A < m_B$

Two similar circular loops carry equal currents in the same direction. On moving the coils further apart,the electric current will

$A$ small bar magnet of dipole moment $M$ is moving with speed $v$ along the $x$-direction towards a small closed circular conducting loop of radius $a$ with its centre $O$ at $x=0$ (see figure). Assume $x >> a$ and the coil has a resistance $R$. Which of the following statement$(s)$ is/are true?

$A$ short magnet is allowed to fall along the axis of a horizontal metallic ring. Starting from rest,the distance fallen by the magnet in one second may be.....$m$

$A$ triangular wire frame (each side $= 2 \, m$) is placed in a region of time-variant magnetic field having $dB/dt = \sqrt{3} \, T/s$. The magnetic field is perpendicular to the plane of the triangle. The base of the triangle $AB$ has a resistance $1 \, \Omega$ while the other two sides have resistance $2 \, \Omega$ each. The magnitude of potential difference between the points $A$ and $B$ will be....$V$