The current through a coil varies according to the following graph. Plot the graph for induced $emf$ versus time for the coil.

The dimensional formula of self-inductance is . . . . . . .

An emf of $2.8 \ mV$ is induced in a rectangular loop of area $150 \ cm^2$ when the current in the loop changes from $3 \ A$ to $8 \ A$ in a time of $0.2 \ s$. Then the self-inductance of the loop is (in $\mu H$)

The unit of self-inductance is:

The current in an inductor is given by $I = (3t + 8)$ $A$,where $t$ is in seconds. The magnitude of the induced emf produced in the inductor is $12 \ mV$. The self-inductance of the inductor is . . . . . . $mH$.

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.)