RL Time Constant Calculator
Enter V, coil resistance and inductance to get the current rise, stored energy and turn-off flyback voltage.
Step-by-step
- Enter valid values to begin.
Ideal inductor with constant L and a lumped series resistance R (no core saturation, no winding capacitance). The switch is a low-side switch, so the switch node rises to V plus the clamp voltage when it opens. The diode drop is treated as constant. The unprotected spike L·I/topen is purely illustrative: in a real circuit it is limited by stray capacitance, avalanche or arcing, not by the assumed opening time. Diode and resistor clamps keep the voltage bounded; the 80% Vds margin is a derating practice, not a standard.
RL Time Constant and Flyback: What Happens When the Switch Opens
Core Engineering Principles
An inductor opposes a change in current, so when voltage is applied the current climbs gradually along i = (V/R)(1 − e−t/τ), with τ = L/R. The R here is the total loop resistance, including the winding’s own DC resistance, which many people forget. The current reaches 63.2% of V/R after one τ and 99.3% after five. A relay pulls in only when the current is high enough to make the force, so what matters is the time to reach a given current, not 5τ.
The dangerous half is turn-off. The inductor stores ½LI² and cannot change its current instantly, so when the switch opens the coil produces whatever voltage is needed to keep current flowing, v = L di/dt. Into an open transistor that means an avalanche that can destroy the part. A flyback diode across the coil gives the current somewhere to go and limits the voltage to about one diode drop. The price is a slow decay, because the coil voltage is only 0.7 V. A resistor clamp or a Zener in series with the diode releases the energy faster, at a higher clamp voltage.
t = −τ ln(1 − I/I∞) • v = L di/dt • τfw = L / (R + Rclamp)
NEC & Standard References
IEEE Std 100 defines inductance, time constant and related terms. IEC 60076 covers power transformers, where the same stored-energy and L/R physics matter at large scale. MOSFET and IGBT datasheets give a drain-source breakdown and an avalanche energy rating, and JEDEC test methods apply, so check your device’s rated Vds and unclamped-inductive-switching energy. The 80% voltage margin used here is practice, not a standard.1. τ = 0.1 / 24 = 4.17 ms; I∞ = 12 / 24 = 500 mA.
2. Time to 300 mA = −4.167 ms × ln(1 − 0.6) = 3.82 ms.
3. Stored energy = ½ × 0.1 × 0.5² = 12.5 mJ.
4. With the diode, the drain rises to 12 + 0.7 = 12.7 V, safe against 60 V. The current takes (L/R) ln(1 + 0.5 × 24 / 0.7) = 12.1 ms to reach zero, and the diode absorbs 1.73 mJ.
5. With a 100 Ω resistor clamp instead: the clamp starts at 50 V, the drain sees 62 V, over the rating.
6. With no protection and an assumed 1 µs opening: L × I / t = 0.1 × 0.5 / 1 µs = 50 kV (illustrative only).
- Diodes slow the release. A relay on a plain flyback diode drops out several times slower; if contact timing matters, add a Zener or resistor in series.
- Wire the diode backwards and nothing happens until the first turn-off. The cathode goes to the positive rail.
- Mind the second spike. Lead inductance and diode recovery add overshoot, so keep the loop tight.
- Inductor saturation breaks the maths. Above the rated current, L collapses and current rises faster than L/R predicts.