Consider the discharging RC circuit (so there is no battery). If the initial charge on the capacitor is Q0. (a) what is the initial current of the system? (b) What is the total energy loss in the resistor? (the quantities R,C, and Q0 are in SI units)

Answer

RC Circuit Discharge: Initial Current and Energy Loss

This explanation focuses on analyzing a discharging RC circuit with no battery. A capacitor with an initial charge Q₀ is allowed to discharge through a resistor R. The capacitor has capacitance C. All values are assumed to be in SI units.

Part (a): Calculating the Initial Current

At the moment the discharge begins (t = 0), the voltage across the capacitor is:

Using Ohm’s Law, the initial current I₀ through the resistor is given by:

Therefore, the initial current is:

Part (b): Total Energy Lost in the Resistor

The total energy initially stored in the capacitor is:

Substituting V₀ = Q₀ / C into the energy formula:

As there is no battery and the capacitor discharges completely, all this energy is dissipated as heat in the resistor. So, the total energy loss in the resistor is:

Summary

• Initial current (I₀): Q₀ / (RC)
• Total energy lost in the resistor: (1/2) × Q₀² / C

These results are essential in understanding transient analysis in electrical circuits, especially when dealing with real-world resistor-capacitor (RC) networks. The principles of energy conservation and time-dependent behavior of circuits are foundational in electronics and physics.