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(B) When a battery of electromotive force $E$ is connected in series with an inductor $L$ and a resistor $R$,the circuit is known as an $RL$ circuit.A

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(B) When a battery of electromotive force $E$ is connected in series with an inductor $L$ and a resistor $R$,the circuit is known as an $RL$ circuit.According to Kirchhoff's voltage law,the equation for the circuit is $E - L \frac{di}{dt} = iR$.Rearranging the terms,we get $\frac{di}{dt} = \frac{E - iR}{L}$.Solving this differential equation with the initial condition that at $t = 0$,$i = 0$,we get the expression for current as a function of time:$i(t) = \frac{E}{R} (1 - e^{-\frac{R}{L}t})$.Here,$i_0 = \frac{E}{R}$ is the maximum steady-state current.The function $i(t) = i_0 (1 - e^{-\frac{R}{L}t})$ represents an exponential growth curve that starts from the origin $(0,0)$ and asymptotically approaches the value $i_0$ as $t$ approaches infinity.Among the given options,the graph in option $B$ correctly depicts this exponential growth behavior.

When a battery is connected across a series combination of self inductance $L$ and resistance $R$,the variation in the current $i$ with time $t$ is best represented by

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