A parallel plate capacitor C with plates of unit area and separation is filled with a liquid of dielectric constant K = 2. The level of liquid is $$\frac{d}{3}$$ initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is

A

$$\frac{6 \varepsilon_0 R}{5d + 3V t}$$

B

$$\frac{(15 d + 9V t) \varepsilon_0 R}{2d^2 - 3dV t - 9V^2t^2}$$

C

$$\frac{6 \varepsilon_0 R}{5d - 3V t}$$

D

$$\frac{(15 d - 9V t) \varepsilon_0 R}{2d^2 + 3dV t - 9V^2t^2}$$