Instructions

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 is fully charged to voltage $$V_0$$ (i.e., charging continues for time $$T \gg RC$$). 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 $$\frac{V_0}{3}$$ and maintained for a charging time $$T \gg RC$$. Then the voltage is raised to $$\frac{2 V_0}{3}$$ without discharging the capacitor and again maintained for a time $$T \gg RC$$. 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.

Question 15

# In Process 1, the energy stored in the capacitor $$E_{C}$$ and heat dissipated across resistance $$E_{D}$$ are related by:

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