A parallel plate capacitor is connected to an ideal battery of emf E through a resistance R and a switch. Area of the plates of capacitor is A, and d is the separation between them. Resistance to the displacement current can be defined as `R_d = V//i_d`, where V and `i_d` are instantaneous potential difference between the plates and displacement current, respectively. Find displacement resistance as a function of time.

Explanation

To find the displacement resistance \( R_d \) as a function of time for a parallel plate capacitor connected to an ideal battery through a resistance \( R \), we can follow these steps:

### Step-by-Step Solution

1. **Understand the Setup**: We have a parallel plate capacitor connected to a battery of emf \( E \) through a resistor \( R \). The area of the plates is \( A \) and the separation between them is \( d \).

2. **Capacitance of the Parallel Plate Capacitor**: The capacitance \( C \) of the parallel plate capacitor is given by:
\[
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