Consider a simple š š¶ circuit as shown in Figure 1.
Process 1: In the circuit the switch š is closed at t = 0 and the capacitor is fully charged toĀ voltage $$V_0$$ (i.e., charging continues for time $$T \gg RC$$). In the process some dissipation $$(E_D)$$Ā occurs across the resistance š . The amount of energy finally stored in the fully chargedĀ capacitor is $$E_c$$.
Process 2: In a different process the voltage is first set to $$\frac{V_0}{3}$$Ā and maintained for a charging time $$T \gg RC$$.Ā Then the voltage is raised toĀ $$\frac{2 V_0}{3}$$Ā without discharging the capacitor and againĀ maintained for a time $$T \gg RC$$.Ā 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:
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