Calculation
i(t) = I0·exp(−R·t/L)
With no further source, coil current decays exponentially to zero through the freewheeling resistor.
Busch 2006, Abschnitt 6.3 Kurzschluss einer stromdurchflossenen Spule, Gl. (6.18): i = I0·e^(−R·t/L), τ = L/R
RL Circuit Current Decay Calculator
With no further source, coil current decays exponentially to zero through the freewheeling resistor.
MINTSI
02
Result
Select a target and calculate.
Coil current i after switch-off versus time t
i(t) = I₀·e^(−t/τ) with τ = L/R: after one time constant the current has fallen to 36.8 %, after 5·τ to below 1 %. A larger freewheeling resistance makes the current decay faster but produces a higher switch-off voltage I₀·R across the coil.
No curve point selected yet.
Understand the inputs
- Coil current i(t) — Current in the RL branch at the selected time after switch-off.
- Initial current I0 — Steady coil current immediately before switch-off, usually U/R of the prior on-state.
- Freewheeling resistance R — Total resistance in the current path during decay, e.g. coil winding plus a connected freewheel resistor.
- Inductance L — Effective coil inductance over the considered current range without saturation.
- Time since switch-off t — Elapsed time from the idealised switch opening at t=0.
Example
I0=4 A, R=6 Ω, L=120 mH and t=40 ms give τ=20 ms and i≈0.541 A.
Assumptions and limits
Ideal freewheel path with no additional voltage source and constant linear inductance; arcing, diode voltage drop and core saturation are excluded.
Understand RL Circuit Current Decay Calculator
This calculator complements RL coil current rise with the reverse process: it determines how fast coil current decays once the source is switched off and current instead flows through a freewheeling resistor.
What does this quantity describe?
If a current-carrying coil is disconnected from its source and short-circuited through resistor R, current decays exponentially as i(t)=I0·exp(−Rt/L). Time constant τ=L/R sets the decay speed; after one τ about 36.8% of I0 remains.
Formula and variables
i(t) = I0·exp(−R·t/L)
i(t) = I0·exp(−R·t/L)τ = L/R
| Symbol / input | Meaning |
|---|---|
| Coil current i(t) | Current in the RL branch at the selected time after switch-off. |
| Initial current I0 | Steady coil current immediately before switch-off, usually U/R of the prior on-state. |
| Freewheeling resistance R | Total resistance in the current path during decay, e.g. coil winding plus a connected freewheel resistor. |
| Inductance L | Effective coil inductance over the considered current range without saturation. |
| Time since switch-off t | Elapsed time from the idealised switch opening at t=0. |
Choose the inputs correctly
I0 is the steady coil current immediately before switch-off, usually from U/R of the prior on-state. R is the resistance in the current path during decay, e.g. winding resistance plus a connected freewheel resistor. L is effective inductance, t the time elapsed since the switch opened.
How to use the calculator
Take I0 from the prior steady operation, e.g. using the current-rise calculator. Use R as the actual freewheeling resistance, not the original series resistor, if the current path changes at switch-off.
Worked example
I0=4 A, R=6 Ω, L=120 mH and t=40 ms give τ=20 ms and i≈0.541 A; after about 5τ=100 ms the current has practically decayed.
Understand the result and units
A smaller freewheeling resistance lengthens τ and thus the decay time. With no freewheel path at all (R→0 at an open switch), a very high induced voltage would theoretically occur, which this simple model does not capture.
I0 and i(t) are currents, R a resistance, L an inductance and t a time. All values are converted internally to coherent SI units.
Typical applications
Estimating decay time for relay, contactor and solenoid-valve coils, and sizing freewheeling resistors or diodes to limit switch-off overvoltage.
Assumptions, limits and common mistakes
Ideal resistive freewheel path with no diode voltage drop or arcing, and constant linear inductance; core saturation and the actual overvoltage at an open switch with no freewheel path are excluded.
Common mistake: Do not use the original series resistor from the on-state for R if a different freewheel path applies at switch-off. Do not forget that with no freewheeling resistance at all, the model assumption is violated.
Frequently asked questions
What is “RL coil current decay on switch-off” used for?
Estimating decay time for relay, contactor and solenoid-valve coils, and sizing freewheeling resistors or diodes to limit switch-off overvoltage.
Where do the input values come from?
I0 is the steady coil current immediately before switch-off, usually from U/R of the prior on-state. R is the resistance in the current path during decay, e.g. winding resistance plus a connected freewheel resistor. L is effective inductance, t the time elapsed since the switch opened.
What does the result not cover?
Ideal resistive freewheel path with no diode voltage drop or arcing, and constant linear inductance; core saturation and the actual overvoltage at an open switch with no freewheel path are excluded.