Question

How much work W is done by the voltage source by the time the steady state is reached?

Express your answer in terms of any or all of E, R, and C.

Answer 1

The work done by the voltage source when the capacitor reaches steady-state is expressed as \( \frac{1}{2} C E^{2} \), where E is the voltage, and C is the capacitance.

Step-by-step explanation:

The work W done by the voltage source when the capacitor reaches the steady-state can be found by considering the energy stored in the capacitor. This is equal to the potential energy Uc given by the formula Uc = \( \frac{1}{2} C E^{2} \), where E is the electric potential (voltage), R is the resistance, and C is the capacitance. In the steady state, the work done by the voltage source to transfer charge until the capacitor is at potential E is equal to the energy stored in the capacitor. Thus, the work done W is \( \frac{1}{2} C E^{2} \).