In the given circuit,the bulb will become suddenly bright if:

Physically,the self-inductance plays the role of

$A$ current vs. time graph of the current passing through a solenoid is shown in the figure. For which time is the back electromotive force $(emf)$ a maximum? If the back $emf$ at $t = 3\;s$ is $e$, find the back $emf$ at $t = 7\;s$, $15\;s$, and $40\;s$. $OA$, $AB$, and $BC$ are straight line segments.

The dimensions of self or mutual inductance are given as

$A$ circular coil consists of $70$ closely wound turns and has a radius of $10 \,cm$. An externally produced magnetic field of magnitude $2 \times 10^{-3} \,T$ is applied perpendicular to the coil. The net flux through the coil is found to vanish when the current in the coil is $2.2 \,A$. The inductance of the coil is: (in $\,mH$)

An air-cored solenoid with length $30 \; cm$,area of cross-section $25 \; cm^{2}$ and number of turns $500$,carries a current of $2.5 \; A$. The current is suddenly switched off in a brief time of $10^{-3} \; s$. How much is the average back $emf$ induced (in $V$) across the ends of the open switch in the circuit? Ignore the variation in magnetic field near the ends of the solenoid.