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 `(2C_(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 2, total energy dissipated across the resistance `E_(D)` is :

Options

A. `E_(D)=3((1)/(2)CV_(0)^(2))`
B. `E_(D)=(1)/(3)((1)/(2)CV_(0)^(2))`
C. `E_(D)=3CV_(0)^(2)`
D. `E_(D)=(1)/(2)CV_(0)^(2)`

Answer

B