RL Circuit Calculator
Time constant and cutoff frequency for a resistor and inductor in series, plus how quickly the current rises and collapses.
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The formula
τ = L ÷ R f_c = R ÷ (2πL) I(t) = I₀ × (1 − e^(−t/τ))
An inductor opposes change in current the way a capacitor opposes change in voltage, so the curve is identical in shape — but resistance appears underneath rather than on top. Raising R in an RC circuit slows it down; raising R in an RL circuit speeds it up.
What to watch out for
Two consequences of L ÷ R being the time constant:
- More resistance is faster. This trips people up coming from RC circuits, where more resistance is slower. Damping resistors on relay coils work for exactly this reason.
- Interrupting the current makes a voltage spike. The energy stored in the field has to go somewhere, and if the switch opens instantly the inductor generates whatever voltage it takes to keep the current flowing — which is why a flyback diode goes across every relay and motor winding.
Frequently Asked Questions
What is the time constant of an RL circuit?
Inductance divided by resistance. 10 mH with 100 Ω gives 100 µs. Use henries and ohms and the answer is in seconds.
Why does more resistance make an RL circuit faster?
Because τ is L ÷ R rather than R × C. The resistance sets the final current, and a higher resistance means a lower final current for the inductor to reach — so it gets there sooner.
Why do inductors need a flyback diode?
Current through an inductor cannot change instantly. Open the switch and the collapsing field produces a large reverse voltage — hundreds of volts from a 12 V relay is normal — which destroys whatever was switching it. A diode gives that current a path to decay through.