Rl Step Response

Open in app →

Step response of a series R-L circuit — current rising toward V/R with time constant τ = L/R.

Series R-L step circuit: a 10 V DC source drives a 10 Ω resistor and a 0.1 H inductor. The loop current is $I_L$; $V_{\mathrm{mid}}$ is the voltage across the inductor.

A 10 V DC source is switched onto a series resistor (10 Ω) and inductor (0.1 H). The inductor opposes the sudden change, so the current rises exponentially rather than jumping: it reaches about 63% of its final value (V/R = 1 A) after one time constant (τ = L/R = 10 ms) and essentially settles after about five. Open it, press Run, and watch the inductor current I_L climb while the inductor voltage V_mid decays from 10 V to zero. Used in the EMT course, Chapter 2 (companion models).

This is the dual of the R-C charge: here it is the current that cannot jump, so I_L is the slow variable and V_mid is its mirror image. At t = 0 the inductor looks like an open circuit (all 10 V across it, I_L = 0); once the current settles it looks like a wire (0 V across it, I_L = 1 A). The run steps at 50 µs over 50 ms so the whole rise is on screen. Note that τshrinks when you add resistance — the opposite of the R-C circuit.