Duration: 8:18

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1

Process \( 1: \) In the circuit the switch \( \mathrm{S} \) is closed at \( t=0 \) and the capacitor if fully charged to voltage \( \mathrm{V}_{0} \) (i.e., charging continues for time \( TR C \) ). In the process some dissipation \( \left(E_{D}\right) \) occurs across the
\( \mathrm{P} \) resistance \( \mathrm{R} \). The amount of energy finally stored in the fully charged capacitor is \( \mathrm{E}_{\mathrm{C}} \).

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Process 2 : In a different process the voltage is first set to \( \frac{\mathrm{V}_{0}}{3} \) and maintained for a charging time
- \( \mathrm{T} \gg \gg \mathrm{RC} \). Then the voltage is raised to \( \frac{2 \mathrm{~V}_{0}}{3} \) without discharging the capacitor and again maintained for
- a time \( \mathrm{T} \gg \mathrm{RC} \). The process is repeated one more time by raising the voltage to \( \mathrm{V}_{0} \) and the capacitor is charged to the same final voltage \( \mathrm{V}_{0} \) as in Process 1 .
These two processes are depicted in figure 2.
Figure 1
In Process 2 , total energy dissipated across the resistance \( E_{D} \) is:
(A) \( \mathrm{E}_{\mathrm{D}}=3\left(\frac{1}{2} \mathrm{CV}_{0}^{2}\right) \)
(B) \( \mathrm{E}_{\mathrm{D}}=\frac{1}{2} \mathrm{CV}_{0}^{2} \)
(C) \( \mathrm{E}_{\mathrm{D}}=3 \mathrm{CV}_{0}^{2} \)
(D) \( \mathrm{E}_{\mathrm{D}}=\frac{1}{3}\left(\frac{1}{2} \mathrm{CV}_{0}^{2}\right) \)
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