Question

A dielectric slab of area A and thickness d is inserted between the plates of capacitor of area 2 A and distance between the plates d with a constant speed v as shown in figure. The capacitor is connected to a battery of emf E. The current in the circuit varies with time as :

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

4

Answer 2

The capacitance of a parallel plate capacitor with partially inserted dielectric varies linearly with the inserted length. Since the dielectric is inserted at a constant speed, the capacitance varies linearly with time. The current in the circuit connected to a constant voltage source is given by $I = E \frac{dC}{dt}$. As $C(t)$ is a linear function of time during insertion, $\frac{dC}{dt}$ is a constant. Thus, the current is constant and positive during insertion. Once the dielectric is fully inserted, the capacitance becomes constant, making $\frac{dC}{dt}=0$, and hence the current drops to zero.