RC Time Constant\ and Discharging Simulation

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Objective

This document explains the transient response of a resistor-capacitor circuit. The central quantity is the RC time constant =RC. The animation shows capacitor voltage, circuit current, current direction, charging, discharging, and the corresponding waveforms on a common timeline.

Circuit Parameters

For the demonstration, V_S=5V, R=1k, C=100 F. Therefore =RC=(1000)(10010^-6) =0.1s.

The initial charging current is I_0=V_SR =5mA.

Charging

For an initially uncharged capacitor, V_C(t)=V_S(1-e^-t/) and i(t)=V_SRe^-t/.

At one time constant, V_C()=V_S(1-e^-1) 0.632V_S, and i()=I_0e^-1 0.368I_0.

Thus at t=, the capacitor has reached approximately 63.2\% of its final voltage.

Discharging

For a capacitor initially charged to V_0, V_C(t)=V_0e^-t/.

Using the charging-current direction as the positive reference, i(t)=-V_0Re^-t/.

The negative sign indicates that the discharge current flows in the opposite direction.

Animation

The following block is interpreted by the NEXMASON Science Viewer.

Interpretation

At the beginning of charging the capacitor behaves approximately like a short circuit, so the current is maximum. As charge accumulates, the capacitor voltage rises and the voltage across the resistor decreases. Therefore the current decreases exponentially.

The RC time constant controls the speed of this process: =RC.

A larger R or a larger C produces a slower transient response.