As shown in the figure, a battery of emf $$\varepsilon$$ is connected to an inductor L and resistance R in series. The switch is closed at $$t = 0$$. The total charge that flows from the battery, between $$t = 0$$ and $$t = t_c$$ ($$t_c$$ is the time constant of the circuit) is:

A

$$\frac{\varepsilon L}{eR^2}$$

B

$$\frac{\varepsilon L}{R^2}\left(1 - \frac{1}{e}\right)$$

C

$$\frac{\varepsilon L}{R^2}$$

D

$$\frac{\varepsilon R}{\varepsilon L^2}$$