Simulate charging and discharging of RC and RL circuits. Visualize voltage and current waveforms with time constant analysis.
Every time a switch closes on a circuit that contains a capacitor or an inductor, the voltages and currents do not land on their final values instantly - they settle along exponential curves paced by a single number, the time constant. This tool takes resistance, capacitance or inductance, and a source voltage, then plots charging and discharging transients for RC and RL circuits and reports the time constant. The usual surprise is the role reversal: an uncharged capacitor acts like a short circuit the instant the switch closes, while an inductor acts like an open circuit, so a capacitor's current starts at its maximum and an inductor's starts at zero.
A concrete input and expected output from the current implementation.
Input
R = 10000 ohm, C = 100 uF, source V = 5 V, charging
Expected output
tau = 1.00 s. Capacitor voltage: 3.16 V at t = 1 s, 4.32 V at t = 2 s, 4.97 V at t = 5 s (99.3% of 5 V). Charging current: 0.50 mA at t = 0, falling to 0.18 mA at t = 1 s.
With tau = R times C = 1.00 s, the voltage follows 5(1 - e^(-t/tau)) V: each elapsed time constant closes 63.2% of the remaining gap to 5 V, so 1 s gives 5(1 - e^(-1)) = 3.16 V and 5 s leaves only about 0.7% of the gap. The current is V/R = 0.50 mA scaled by the same decaying factor e^(-t/tau).
The tool computes tau = R times C for a capacitor circuit and tau = L divided by R for an inductor circuit. Charging follows v(t) = V(1 - e^(-t/tau)), and each time constant closes 63.2 percent of the remaining gap to the final value; after five time constants the quantity is within about 0.7 percent of it. Discharging follows V e^(-t/tau) from the starting stored value.
Intuition fails at the first instant. Because a capacitor's voltage cannot change discontinuously, an uncharged capacitor at t = 0 passes the full source current V/R and builds voltage from zero, the current decaying as the voltage rises. Because an inductor's current cannot change discontinuously, its current starts at zero and climbs toward V/R while the inductor voltage collapses; charging and discharging are the two directions of the same exponential.
No, it never exactly reaches its limit; each time constant closes 63.2 percent of the remaining gap, so the value approaches the asymptote without arriving. After 5 tau it is within about 0.7 percent, which is why five time constants is the standard rule of thumb for "settled". The plotted curve therefore ends just under the final value, not on it.
It depends on the circuit, which is the trap. For RC, tau = RC, so a larger resistor slows the charge. For RL, tau = L/R, so a larger resistor makes the current settle faster. If that seems backwards, notice the time constant is a product for capacitors and a quotient for inductors; the same knob moves the two circuits in opposite directions.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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