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 $$V0$$ (i$$.e., charging continues for time T$$RC). In the process some dissipation ED occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is EC .Process $$2$$: In a different process the voltage is first set to $$V03$$ and maintained for a charging time TRC. Then the voltage is raised to $$2V03$$ without discharging the capacitor and again maintained for a time TRC. The process is repeated one more time by raising the voltage to $$V0$$ and the capacitor is charged to the same final voltage $$V0$$ as in Process $$1$$.These two processes are depicted in Figure $$2$$. In Process $$1$$, the energy stored in the capacitor EC and heat dissipated across resistance ED are related by:In Process $$2$$, total energy dissipated across the resistance ED is:

Question

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 $$V0$$ (i$$.e., charging continues for time T>>$$RC). In the process some dissipation ED  occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is EC .Process $$2$$: In a different process the voltage is first set to  $$V03$$ and maintained for a charging time T>>RC. Then the voltage is raised to  $$2V03$$ without discharging the capacitor and again maintained for a time T>>RC. The process is repeated one more time by raising the voltage to $$V0$$  and the capacitor is charged to the same final voltage $$V0$$ as in Process $$1$$.These two processes are depicted in Figure $$2$$. In Process $$1$$, the energy stored in the capacitor EC and heat dissipated across resistance ED are related by:In Process $$2$$, total energy dissipated across the resistance ED is:

Infinity Learn · Accepted Answer

$$Ec=12CV02W=qV0=CV02$$⇒$$ED=W$$−$$EC=12CV02=EC$$ Total energy supplies in three stages $$=CV03V03+CV032V03+CV03V0=23CV02$$ Energy storages in cap  $$=12CV02Therefore$$, loss across R  $$=23CV02-12CV02=16CV02=1312CV02$$  Hence, ‘A’

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