$(a)\;\frac{eR^2E}{L} \\ (b)\;E \bigg(\frac{L}{R}\bigg) \\(c)\;\frac{EL}{eR^2} \\(d)\;\frac{eL}{ER} $

The current flowing in LR circuit at a given time t is

$i= i_0 (1-e^{-t/T})$

$i_0=\large\frac{E}{R}$ and $T=\large\frac{L}{R}$

Charge flowing in time $t=T$

$q=\int \limits_0^T idt$

$\quad= \int \limits_0^r i_0 (1-e^{-t}{r})dt$

$\qquad= \large\frac{i_0T}{e}$

$\qquad= \large\frac{\Large\frac{E}{R} \frac{L}{R}}{e}$

$\qquad= \large\frac{EL}{R^2e}$

Hence C is the correct answer.

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