$A$ branch of a circuit is shown in the figure. If the current is decreasing at the rate of $10^3 \ A \ s^{-1}$, then the potential difference between $A$ and $B$ is (in $V$)

The ratio of the number of turns per unit length of two solenoids $A$ and $B$ is $1: 3$ and the lengths of $A$ and $B$ are in the ratio $1: 2$. If the two solenoids have the same cross-sectional area,the ratio of the self-inductances of the solenoids $A$ and $B$ is

Consider a toroid with a rectangular cross-section,of inner radius $a$,outer radius $b$,and height $h$,carrying $n$ number of turns. Then the self-inductance of the toroidal coil when current $I$ is passing through the toroid is:

The self-induced $e.m.f.$ in a $0.1 \, H$ coil when the current in it is changing at the rate of $200 \, A/s$ is......$V$

When the current in a coil changes from $8 \; A$ to $2 \; A$ in $3 \times 10^{-2} \; s$,the $e.m.f.$ induced in the coil is $2 \; V$. The self-inductance of the coil (in $mH$) is:

The current through a coil of self-inductance $L = 2 \ mH$ is given by $I = t^2 e^{-t}$ at time $t$. How long will it take for the induced electromotive force $(emf)$ to become zero (in $s$)?