The current flowing through an inductor of self-inductance $L$ is continuously increasing at a constant rate. The variation of induced e.m.f. $(e)$ versus $dI/dt$ is shown graphically by which figure?

In an inductor,the current $I$ varies with time $t$ as $I = 5 \,A + 16 \,(A/s) \,t$. If the induced emf in the inductor is $5 \,mV$,the self-inductance of the inductor is .............. $\times 10^{-4} \,H$.

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.)

With the help of $L = \frac{N\phi}{I}$ and $\varepsilon = -L\frac{dI}{dt}$,give two definitions of self-inductance.

$A$ 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 $V$)

An inductor coil wound uniformly has self-inductance $L$ and resistance $R$. The coil is broken into two identical parts. The two parts are then connected in parallel across a battery of $E$ volt of negligible internal resistance. The current through the battery at steady state is