Rc Charging

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Charging of a series R-C circuit — capacitor voltage rising toward the source with time constant τ = RC.

Series R-C charging circuit: a 10 V DC source drives a 1 kΩ resistor into a 10 μF capacitor. The charging current is $I_C$ and the capacitor voltage is $V_{\mathrm{cap}}$.

A 10 V DC source charges a capacitor (10 μF) through a series resistor (1 kΩ). The capacitor voltage cannot change instantly, so it rises exponentially toward the source voltage, reaching about 63% after one time constant (τ = RC = 10 ms) and nearly 100% after five. The charging current I_C starts at V/R = 10 mA and decays to zero as the capacitor fills. Open it, press Run, and watch V_cap charge while I_C falls away. Used in the EMT course, Chapter 2 (companion models).

V_cap and I_C are exact mirror images: as the voltage climbs the current falls, because the resistor only sees the difference between the source and the capacitor. The run uses a 50 µs step over 50 ms — five time constants — so you see the curve start steep, pass 6.3 V at 10 ms, and flatten to 10 V. Shrink the capacitor or the resistor and τ shrinks with it; the same shape appears, just faster.