IIT JEE Advanced 2008 Paper 2

The effective capacitance
Ceff =

Aε0

d−y+( y εr )

where A is the area of the capacitor plate, d is the plate separation, y is the thickness of dielectric and εr is the dielectric constant. It is given that rate of change of dielectric liquid is

dy

dt

= - V ⇒ y = -- Vt + C1
At t = 0, we have
y =

d

3

⇒ C1 =

d

3

Therefore,
Ceff =
=

ε0εr [d(2εr+1)+3V(εr−1)]

3

=

6ε0

5d+3Vt

The time constant is
τ = RCeff =

6ε0R

5d+3Vt