The figure below shows a battery of emf $\epsilon$ connected to an inductor $L$ and a resistance $R$ in series. If the switch is closed at $t=0$, then the total charge that flows from the battery in one time constant of the circuit is

• A

  $\frac{\epsilon L}{R^2}\left(1-\frac{1}{\mathrm{e}}\right)$
• B

  $\frac{\epsilon L}{2\mathrm{e}{R}^2}$
• C

  $\frac{\epsilon L}{4\mathrm{e}{R}^2}$
• Correct answer
  D

  $\frac{\epsilon L}{\mathrm{e}{R}^2}$

Hence, the correct answer is option: 'D'.