Inputs
Formula
For a step from 0 to Ifinal in an RL series circuit:
i(t) = Ifinal · (1 − e−t/τ)
Time constant:
τ = L / R
Time to reach 90% of final value:
t90% = τ · ln(10) = (L/R) · ln(10)
ln(10) ≈ 2.302585093
Worked Example
Given R = 100 Ω and L = 10 mH:
τ = L/R = 0.01 / 100 = 0.0001 s = 0.1 ms
t90% = τ · ln(10) ≈ 0.1 ms · 2.302585093 ≈ 0.2303 ms
Change inputs above to match your circuit values and recalculate.
FAQs
τ = L/R is the time constant at which the response reaches about 63.2%. t90% = τ·ln(10) is the time to reach 90% of the final value.
The formula shown targets current rise. The inductor voltage decays exponentially after the step. Use circuit equations accordingly if you need voltage timing instead of current.
It is accurate for linear components and small-signal operation. Core saturation, series resistance of the inductor, and source limits can alter the effective time constant.
Yes. Use t = −τ ln(1 − p) where p is the fraction between 0 and 1. For example, 95% uses ln(20); 99% uses ln(100).
Inductance and resistance vary with temperature and frequency. Significant changes in either parameter change τ, which directly scales t90%.