In the part of an a.c. circuit as shown,the resistance $R=0.2 \ \Omega$. At a certain instant,$(V_{A}-V_{B})=0.5 \ V$,$I=0.5 \ A$ and $\frac{dI}{dt}=8 \ A/s$. The inductance of the coil is (in $H$)

$A$ coil has $N$ turns and the current passing through it is $I$ ampere,resulting in a self-inductance of $L$ Henry. If the current changes to $5I$ $A$,the new self-inductance will be . . . . . . $H$.

The $SI$ unit of inductance,the henry,cannot be written as:

$A$ 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.

In which circuit will the current be maximum immediately after closing the switch $S$?

An air-cored solenoid with $30 \ cm$ length,area of cross-section $25 \ cm^2$,and $500$ turns 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 across the ends of the open switch in the circuit (in $V$)? (Ignore the variation in magnetic field near the ends of the solenoid.)