RL Step Response

The RL Circuit: Step Response

An inductor resists changes in current — the dual of a capacitor, which resists changes in voltage.

When a voltage Vs is suddenly applied to a series RL circuit:

Vs ---[R]---[L]--- GND

The current builds up exponentially:

I(t) = (Vs / R) · (1 − e^(−t / τ))

Where τ = L / R is the time constant (seconds).

The Duality with RC

Time Constant τ = L/R

At t = τ: I = (Vs/R) · (1 − 1/e) ≈ 63.2% of final current

Physical Intuition

The inductor's voltage is V_L = L · dI/dt. Initially, current is zero and V_L = Vs (all voltage across inductor). As current builds up, the voltage drop across R increases, reducing V_L, which slows the rate of change of current.

Applications

• Motor drivers (inductors are motor windings)
• Switching power supplies
• RF filters and chokes
• Flyback converters

Your Task

Implement double rl_step(double vs, double r, double l, double t) that returns the current I(t) for a series RL circuit with step voltage Vs.

Use #include <math.h> for exp.