LearnTronics

RL Transient Response

Tutorial Index

Recipe #36 — rl transient response

The capacitor time constant has an inductor cousin. In a series RL circuit, current rises gradually because the growing magnetic field opposes rapid change.

Close SW1: current does not jump instantly to V/R. The inductor develops a voltage that initially opposes the increase in current. As the magnetic field builds, the current approaches its final value.

τ = L / R

i(t) = (V/R)(1 − e^−t/τ)

Compare capacitor and inductor behavior

A capacitor resists a sudden change in voltage. An inductor resists a sudden change in current. Both create exponential transients, but the electrical quantity that cannot jump instantly is different.

Resistance shortens the RL time constant

Because τ = L/R, more series resistance makes the inductor current settle faster, not slower. That is the opposite algebraic placement from RC timing, where τ = RC.

Try these yourself

Which quantity cannot change instantaneously in an ideal inductor? Current Resistance Time Wire color

An ideal inductor develops whatever voltage is needed to oppose an instantaneous change in its current.

What is the RL time constant? L/R RC R/L LC

For a simple series RL circuit, tau equals inductance divided by resistance.

Approximately what fraction of final current is reached after one time constant? 63% 1% 200% Exactly zero

The exponential rise reaches about 63.2% of its final value at t = tau.

< Relay Buzzer | Inductive Flyback in Depth >