An inductor of inductance $$L = 400$$ mH and resistors of resistances $$R_1 = 2\Omega$$ and $$R_2 = 2\Omega$$ are connected to a battery of emf $$12$$ V as shown in the figure. The internal resistance of the battery is negligible. The switch $$S$$ is closed at $$t = 0$$. The potential drop across $$L$$ as a function of time is

A

$$6e^{-5t}$$ V

B

$$\frac{12}{t}e^{-3t}$$ V

C

$$6\left(1 - e^{-t/0.2}\right)$$ V

D

$$12e^{-5t}$$ V