Consider a simple RC circuit as shown in figure
1. Process 1: In the circuit the switch S is closed at t=0 and the capacitor if fully charged to voltage `V_0` (i.e., charging continues for time T`gt gt` RC). In the process some dissipation (`E_D`) occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is `E_c`
Process 2 : In a different process the voltage is first set to `(V_0)/(3)` and maintained for a charging time `T gt gt RC`. Then the voltage is raised to `(2V_0)/(3 )` without discharging the capacitor and again maintained for a time T`gt gt` RC. The process is repeated one more time by raising the voltage to `V_0` and the capacitor is charged to the same final voltage `V_0` as in Process 1.
These two processes are depicted in figure 2.

In Process 1, the energy stored in the capacitor `E_C` and heat dissipated across resistance `E_D` are related by:

Options

A. `E_c =1/2 E_D`
B. `E_C =2E_D`
C. `E_C=E_D`
D. `E_C =E_D ln 2`

Answer

C