RL Circuit Time Constant Calculator

RL time constant: τ = L / R

The RL time constant τ = L / R tells you how quickly current builds up in an inductor once a voltage step hits it: i(t) = If · (1 − e−t/τ). The thing about inductors is that they fight changes in current. They hold energy in a magnetic field, and if you cut the current abruptly you get a high-voltage spike (V = −L · di/dt). Take a quick example: with R = 10 Ω and L = 10 mH you get τ = 1 ms. The current hits 63 % of its final value after 1 ms and is basically saturated by 5 ms.

Applications: motors, solenoids, switching supplies

You see RL behaviour everywhere: motor inrush current, the actuation timing of solenoids and relays, the flyback transformer that sits at the heart of switching supplies, and ignition coils. Put a flyback diode across the inductor to clamp that turn-off spike, otherwise the switching transistor takes the hit.

FAQ

Why does τ grow with L and shrink with R? A bigger L stores more energy per ampere. A bigger R burns that energy off faster, so current rises (or decays) more quickly.

Why does opening an inductive circuit cause arcing? The inductor refuses to let the current drop, so it generates V = −L · di/dt. Switch off fast enough and you can see hundreds or thousands of volts jump across the contacts.

Do I always need a flyback diode? If a transistor or MOSFET is driving an inductive load, yes. Skip it and the spike will usually kill the switch on the very first turn-off.