RL Time Constant Calculator — τ = L/R, Settling Time & Back-EMF

Calculate

Series inductance. Relay coil: 10–500 mH; power-supply inductor: 10–500 μH; brake coil: 0.5–10 H.

Total series resistance — inductor DCR plus any external resistor. Use DCR from the inductor datasheet.

DC source voltage across the RL series combination. Common: 5 V (logic), 12 V (automotive), 24 V (industrial). Enter 0 for pure time-constant analysis.

Fundamental circuit mode — affects current direction and protection relevance.

Safety-relevant: affects HIGH-BACK-EMF status and protection guidance.

Analysis time, target τ, switch and clamp details, component tolerances (all optional)

Overview

The RL Time Constant Calculator computes τ = L/R and the complete first-order DC transient response of a series RL circuit. Enter inductance, resistance, and supply voltage to get: the time constant in seconds, steady-state current V/R, 5τ settling time, energy stored ½·L·I², first-order characteristic frequency R/(2π·L), back-EMF screening estimate at abrupt switch opening, and resistive dissipation.

Results are classified via two independent tracks — Track A for the primary operating condition (NORMAL, HIGH-STORED-ENERGY, HIGH-BACK-EMF, HIGH-DISSIPATION, OUT-OF-SPEC, or INFEASIBLE), and Track B for electrical response speed (ULTRA-FAST through SLOW).

This calculator supports Analysis mode and Design Verification mode. Analysis mode is the default — enter L, R, and V to characterize the circuit. Design Verification mode activates when you supply a Target Time Constant; the calculator computes deviation from target and the L or R value needed to hit it.

Application contexts covered include relay coils, solenoid actuators, brake-release coils, EMI chokes (educational framing only), switching-converter inductors (educational only), and general first-order RL transient analysis. Out of scope: AC steady-state analysis, coupled networks, saturation modeling, core loss, and functional-safety stopping-time verification for brakes.

How to Use This Calculator

  1. Enter inductance L — select the unit (mH, μH, nH, or H) and enter the value. Relay coils: 10–500 mH; power-supply inductors: 10–500 μH; brake coils: 0.5–10 H.

  2. Enter resistance R — total series resistance including the inductor DCR plus any external resistor. Select the unit (Ω, mΩ, or kΩ).

  3. Enter supply voltage V (DC) — the DC voltage across the RL combination. Leave blank or enter 0 for pure time-constant analysis without steady-state current.

  4. Click Calculate — get τ, I_ss, 5τ settling time, energy stored, back-EMF screening estimate, dissipation, characteristic frequency, and the combined Track A / Track B status badge.

  5. Open advanced parameters to add target τ for Design Verification mode, specify transient mode (energize or de-energize), add switch open time for a sharper back-EMF estimate, or select a protection device.

  6. Review the status badge — Track A flags physical operating conditions (NORMAL, HIGH-STORED-ENERGY, HIGH-BACK-EMF, HIGH-DISSIPATION, OUT-OF-SPEC, INFEASIBLE); Track B classifies response speed (ULTRA-FAST through SLOW).

All electrical quantities use SI units internally. The inductance unit selector converts your entry to henries; resistance to ohms. Supply voltage affects steady-state current and energy — it does not change τ = L/R.

Inputs & Outputs

Inputs

Required

  • •Inductance (L) — Series inductance with unit selector (mH, μH, nH, H). Typical: relay coil 10–500 mH; power-supply inductor 10–500 μH; brake coil 0.5–10 H.
  • •Resistance (R) — Total series resistance with unit selector (Ω, mΩ, kΩ). Include the inductor's own DCR from the datasheet plus any external resistor.
  • •Supply Voltage (V) — DC source voltage across the RL combination. Common: 5 V (logic), 12 V (automotive/relay), 24 V (industrial), 48 V (telecom). Enter 0 for pure time-constant analysis.

Mode Selectors

  • •Transient Mode — Energize (current rises toward I_ss) or De-energize (current decays toward zero). Affects the transient snapshot table.
  • •Protection Device — None, Flyback Diode, TVS/Zener Clamp, MOV, RC Snubber, or Active Clamp. When a device other than None is selected, the HIGH-BACK-EMF flag is suppressed.
  • •Application Context — Optional context for application-specific guidance: General, Relay Coil, Solenoid, Brake Coil, EMI Choke, or Power Supply Inductor. Affects pedagogy and warning thresholds, not math.

Advanced (Optional)

  • •Analysis Time (t) — Specific time for transient evaluation with unit selector (ms, μs, ns, s). Leave blank for the standard 1τ–5τ snapshot table.
  • •Initial Current (I₀) — Starting current at t = 0 (A). For de-energize from a pre-charged inductor, enter the current present before the switch opens. Visible only in De-energize mode.
  • •Target Time Constant (τ) — Target τ with unit selector (ms, μs, ns, s). Activates Design Verification mode — calculator reports deviation from target and the L or R adjustment needed.
  • •Switch Open Time — Time the circuit interrupter takes to open, with unit selector (ms, μs, ns). Sharpens the back-EMF screening estimate. Mechanical switch ≈ 1 ms; semiconductor ≈ 100 ns. Default: 1 ms mechanical.
  • •Switch Voltage Rating (V) — Maximum voltage rating of the switching element (MOSFET Vds, relay contact, BJT Vce). When provided, back-EMF estimate is compared to this rating and can trigger HIGH-BACK-EMF.
  • •Inductance Tolerance (%) — Inductor tolerance from datasheet (typical ±10%, ±20%). Used in Design Verification mode to compute the realistic τ deviation band.
  • •Resistance Tolerance (%) — Resistor tolerance from datasheet (typical ±1%, ±5%). Used together with inductance tolerance for τ band in Design Verification mode.

Outputs

Primary Results

  • •Time Constant (τ) — L/R in seconds, displayed with magnitude scaling (μs, ms, or s). Core result of the calculator.
  • •Steady-State Current — V/R in amperes, displayed with magnitude scaling (μA, mA, or A). Current the circuit approaches after 5τ.
  • •Settling Time (5τ) — 5 × τ in seconds, magnitude-scaled. Time to reach 99.3% of steady state — the conventional engineering threshold for 'settled.'
  • •Energy Stored (steady state) — ½ × L × I_ss² in joules, magnitude-scaled (μJ, mJ, J). Energy in the magnetic field at steady state. Drives HIGH-STORED-ENERGY flag when ≥ 10 J.
  • •Resistive Dissipation — V² / R in watts. Continuous power dissipated in the series resistance. Drives HIGH-DISSIPATION flag when ≥ 10 W.
  • •Characteristic Frequency (f_c) — R / (2π × L) in Hz — the −3 dB point of the first-order RL response. Magnitude-scaled (Hz, kHz).
  • •Back-EMF Screening Estimate — L × I_ss / t_switch_open in volts. First-order estimate of the inductive voltage spike at switch opening. Uses the entered switch open time or 1 ms mechanical default.

Status Classification

  • •Circuit Status (Track A) — Physical operating condition: NORMAL, HIGH-STORED-ENERGY (W ≥ 10 J), HIGH-BACK-EMF (V_kickback ≥ 100 V or 100× supply, no protection), HIGH-DISSIPATION (P ≥ 10 W), OUT-OF-SPEC (>20% deviation from target τ), or INFEASIBLE (L or R = 0).
  • •Electrical Response Speed (Track B) — Response speed classification by τ: ULTRA-FAST (τ < 1 μs), VERY-FAST (1 μs – 1 ms), FAST (1 ms – 100 ms), MEDIUM (100 ms – 1 s), SLOW (τ ≥ 1 s).

Design Verification (when target τ entered)

  • •Deviation from Target τ (%) — Signed percent deviation of computed τ from the target. Positive = τ is larger than target; negative = smaller. OUT-OF-SPEC triggers when absolute deviation exceeds 20%.
  • •L Needed (R fixed) — Inductance value (H) required to hit the target τ exactly, keeping R unchanged.
  • •R Needed (L fixed) — Resistance value (Ω) required to hit the target τ exactly, keeping L unchanged.

Formula

Core Formula

Time Constant:

τ = L / R [seconds]

Steady-State Current:

I_ss = V / R [amperes]

Energize Transient (switch closes at t = 0):

i(t) = I_ss × (1 − e^(−t/τ))
V_R(t) = i(t) × R
V_L(t) = V − V_R(t)

De-energize Transient (decay through the freewheel path):

i(t) = I_initial × e^(−t/τ)

Settling Time:

t_settle = 5τ (99.3% of final value)

Energy Stored:

W_L = ½ × L × I_ss² [joules]

Resistive Dissipation:

P_R = V² / R = I_ss² × R [watts]

First-Order Characteristic Frequency:

f_c = R / (2π × L) [Hz]

Back-EMF Screening Estimate:

V_kickback ≈ L × I_ss / t_switch_open [V]

This is a first-order screening estimate only. Real peak voltage is bounded by parasitic capacitance, switch breakdown, and arc formation.

Design Verification (when target τ provided):

deviation = (τ − τ_target) / τ_target × 100 [%]
L_target = τ_target × R (keep R fixed)
R_target = L / τ_target (keep L fixed)

Variables

Variable Meaning Units
L Inductance H
R Total series resistance Ω
V DC supply voltage V
τ Time constant (L/R) s
I_ss Steady-state current A
t_settle 5τ settling time s
W_L Energy stored in inductor J
P_R Resistive dissipation W
f_c First-order characteristic frequency Hz
V_kickback Back-EMF screening estimate V

What Is the RL Time Constant

The RL time constant τ is the single number that describes how fast current in a series resistor-inductor circuit responds to a change in applied voltage. Defined as τ = L/R, it has units of seconds because the henry divides cleanly by the ohm. Larger τ means slower response; smaller τ means faster response.

The physical reason τ exists is Lenz's law, expressed mathematically by Faraday's law of induction. An inductor opposes changes in current. When you connect a battery to an RL series circuit, current cannot jump instantly to V/R — the inductor generates a back-EMF proportional to di/dt that opposes the rising current. As current rises, V_L falls, di/dt decreases, and current approaches I_ss asymptotically. The exponential time scale is governed entirely by L/R.

After one time constant, current reaches 63.2% of its final value. After five time constants, 99.3% — the conventional engineering threshold for "settled." The same τ governs both energize and de-energize transients, so a relay coil with τ = 50 ms takes about 250 ms to fully energize and 250 ms to fully discharge through a flyback diode.

The inductor stores energy W_L = ½·L·I² in its magnetic field during steady-state operation. This energy must go somewhere when current is interrupted — which is the origin of inductive kickback. The back-EMF estimate V ≈ L·I/Δt gives an order-of-magnitude prediction; real peaks are bounded by stray capacitance and breakdown paths.

How to Calculate RL Time Constant

The RL time constant calculation requires only two values: inductance in henries and total series resistance in ohms.

τ = L / R

For a 200 mH relay coil with 400 Ω winding resistance: τ = 0.200 / 400 = 0.0005 s = 500 μs. After 500 μs, the coil current reaches 63.2% of its final value. After 5 × 500 μs = 2.5 ms, it is within 0.7% of steady state.

After converting L to henries and R to ohms, these unit shortcuts are convenient:

  • L in mH and R in Ω → τ in milliseconds. Example: 100 mH / 50 Ω = 2 ms.
  • L in μH and R in Ω → τ in microseconds. Example: 47 μH / 10 Ω = 4.7 μs.
  • L in μH and R in mΩ → τ in milliseconds. Example: 10 μH / 5 mΩ = 2 ms.

RL Circuit Current Rise and Transient Table

When you close the switch on a series RL circuit, current rises from zero toward V/R:

i(t) = I_ss × (1 − e^(−t/τ)) where I_ss = V / R

At well-defined multiples of τ, current reaches these percentages of the final value:

Time Current (% of I_ss) Remaining Error
1τ 63.2% 36.8%
2τ 86.5% 13.5%
3τ 95.0% 5.0%
4τ 98.2% 1.8%
5τ 99.3% 0.7%
7τ 99.9% 0.09%

These percentages are universal — they apply to every RL circuit, from a relay coil to a power brake.

Back-EMF and Inductive Kickback

When the switch opens on an energized RL circuit, the inductor refuses to let current change instantly. The stored energy W = ½·L·I² must go somewhere. Without a clamp path, the inductor drives whatever voltage is needed to keep current flowing — often hundreds or thousands of volts.

The screening formula gives an order-of-magnitude prediction:

V_kickback ≈ L × I / t_switch_open

For a 100 mH coil at 100 mA, opened by a MOSFET in 100 ns:

V_kickback ≈ 0.100 × 0.100 / 0.0000001 = 100,000 V

This will never appear on a scope — the MOSFET avalanches at its 30 V Vds rating, dumping inductor energy into the silicon. Over hundreds of switching cycles, the MOSFET fails. The fix is a flyback diode (1N4007 for signal relays) reverse-biased across the inductor coil.

Protection Device Selection

Four common devices manage inductive transients differently:

Flyback diode — clamps at ~0.7 V, slowest release. Best for DC relay coils where slow drop-out is acceptable. Standard practice for microcontroller GPIO outputs.

TVS or Zener clamp — clamps at a chosen voltage (5–400 V typical). Faster release than a plain diode because the higher clamp voltage forces faster di/dt. Best for brake coils and fast-cycling relays.

RC snubber — damps ringing and reduces dV/dt. Best for AC circuits and contacts where arcing erosion is the main concern. Snubber design requires the measured ringing frequency.

MOV (metal-oxide varistor) — wide-range clamping with high joule absorption. Best for industrial line-side protection and large coils with significant stored energy. Verify joule rating against W_L.

Common Values Reference

Component Type Inductance Range DC Resistance Range Typical τ
Signal relay coil 10–500 mH 50–1,000 Ω 0.5–10 ms
Power relay coil 50 mH–2 H 50–500 Ω 1–100 ms
Small solenoid (12 V) 50–500 mH 5–80 Ω 6–100 ms
Large solenoid / contactor 100 mH–5 H 20–500 Ω 10 ms–500 ms
Brake coil (industrial) 0.5–10 H 1–50 Ω 100 ms–10 s
Power-supply inductor 1–500 μH mΩ to a few Ω 0.1 μs–5 ms
Signal choke 10 μH–10 mH mΩ to tens of Ω 1 μs–100 ms

If your inputs are far outside these ranges, double-check the unit selector — the most common error is entering mH when μH was intended, producing a 1000× wrong τ.

Key Facts

  • The RL time constant τ = L/R has units of seconds when L is in henries and R is in ohms — henry divided by ohm equals volt·second/ampere divided by volt/ampere = second.
  • After 1τ, current reaches 63.2% of its steady-state value. After 5τ, 99.3%. These percentages apply identically to both energize and de-energize transients.
  • Supply voltage V does not affect τ. Doubling V doubles I_ss and quadruples stored energy, but the same L/R governs how fast current changes.
  • Energy stored in the inductor at steady state is W = ½·L·I². A 10 H brake coil at 24 A stores 2,880 J — comparable to a falling object.
  • An abrupt switch interruption without a clamp can produce back-EMF voltages many times the supply. Logic-level MOSFETs (20–30 V Vds) and MCU GPIO pins are common casualties.
  • A flyback diode clamps back-EMF to ~0.7 V but slows de-energize current decay. TVS or Zener clamping at a higher voltage gives faster release at the cost of higher voltage stress.
  • The first-order characteristic frequency f_c = R/(2π·L) is the −3 dB point of the simple RL response — useful intuition, not a complete EMI filter specification.
  • Design Verification mode: if target τ falls within the component tolerance band (computed from L tolerance and R tolerance), the nominal design is acceptable within manufacturing variation.

Applications

  • Relay coil energize/de-energize timing and back-EMF protection screening.
  • Solenoid actuator response time estimation and PWM overdrive planning.
  • Brake coil release time verification and clamp device selection.
  • First-pass EMI choke frequency analysis (educational — not a full EMI filter specification).
  • Switching-converter inductor current-change intuition (educational — not a ripple-current inductor selection method).
  • General first-order RL transient education and circuit analysis.
  • Design Verification: checking whether a chosen L and R combination meets a target time constant within component tolerance.
  • Back-EMF screening for MOSFET and BJT gate driver circuits driving inductive loads.

Example Calculation

Example 1 — Relay Coil: τ, Back-EMF, and Status

Given:

  • L = 200 mH (relay coil)
  • R = 400 Ω (coil winding resistance)
  • V = 24 V DC
  • No switch open time entered (calculator uses mechanical 1 ms default for estimate)

Computed values:

τ = 0.200 / 400 = 0.0005 s = 500 μs
I_ss = 24 / 400 = 0.060 A = 60 mA
t_settle = 5 × 500 μs = 2.5 ms
W_L = ½ × 0.200 × 0.060² = 360 μJ
P_R = 24² / 400 = 1.44 W
f_c = 400 / (2π × 0.200) ≈ 318 Hz
V_kickback (mech 1 ms) = 0.200 × 0.060 / 0.001 = 12 V

Result: NORMAL / VERY-FAST

Track A = NORMAL: all physical checks pass. Track B = VERY-FAST: τ = 500 μs falls in the 1 μs–1 ms range. The 12 V back-EMF estimate at mechanical switch opening is below 100 V and below 100× supply, so no HIGH-BACK-EMF flag. The 1.44 W dissipation is well below 10 W. A 1N4148 or 1N4007 flyback diode is standard practice to protect the switching element.

Example 2 — Design Verification (OUT-OF-SPEC)

Given:

  • L = 100 mH, R = 50 Ω, V = 12 V
  • Target τ = 1 ms (Design Verification mode)

Computed values:

τ = 0.100 / 50 = 0.002 s = 2 ms
deviation = (2 − 1) / 1 × 100 = +100%
L_target (R = 50 Ω) = 0.001 × 50 = 50 mH
R_target (L = 100 mH) = 0.100 / 0.001 = 100 Ω
P_R = 144 / 50 = 2.88 W

Result: OUT-OF-SPEC / FAST

Deviation +100% far exceeds the ±20% threshold. To hit the 1 ms target: L = 50 mH (keeping R = 50 Ω) or R = 100 Ω (keeping L = 100 mH) — note that raising R to 100 Ω also halves the steady-state current from 240 mA to 120 mA, which may matter for relay pickup or holding force.

Example 3 — Industrial Brake Coil: HIGH-STORED-ENERGY

Given:

  • L = 10 H, R = 2 Ω, V = 48 V
  • No protection device

Computed values:

τ = 10 / 2 = 5 s
I_ss = 48 / 2 = 24 A
t_settle = 5 × 5 = 25 s
W_L = ½ × 10 × 24² = 2,880 J
P_R = 2,304 / 2 = 1,152 W
V_kickback (mech) > 10 kV (estimate capped)

Result: HIGH-STORED-ENERGY / SLOW

W_L = 2,880 J triggers Track A = HIGH-STORED-ENERGY. Three concerns must be addressed: (1) a controlled discharge path rated for 2,880 J, (2) a contactor with sufficient voltage and current breaking rating, (3) a thermal solution for 1,152 W continuous winding dissipation. This is a serious industrial design requiring brake-manufacturer application notes and relevant functional-safety standards.

Standards & References

  • IEC 60050-131:2002 — International Electrotechnical Vocabulary, Part 131: Circuit theory. Defines time constant, transient response, RL circuit, and related foundational terminology.
  • IEC 60115-1:2020 — Fixed resistors for use in electronic equipment, Part 1: Generic specification. Provides the resistor power derating practice (50% for general use) used in this calculator's HIGH-DISSIPATION threshold.
  • IEC 60664-1:2020 — Insulation coordination for equipment within low-voltage supply systems. Relevant when back-EMF transients approach insulation withstand levels. This calculator does not perform insulation coordination.
  • IEC 61810-1:2015 — Electromechanical elementary relays, Part 1: General and safety requirements. Reference standard for relay coil specifications including coil resistance, rated current, and contact ratings.
  • MIT OCW — Transient Analysis of First Order RC and RL Circuits — Clean derivation of the L·di/dt + Ri = V solution with worked examples.
  • Altium — Using Flyback Diodes in Relays — Practical discussion of flyback diode selection for relay coils and motor driver circuits.
  • BIPM SI Brochure — The henry (H) SI derived unit of inductance: 1 V·s/A.

Limitations

  • Saturation is not modeled — real inductors lose inductance sharply when current exceeds the rated saturation current I_sat from the datasheet. Verify I_ss is below I_sat with at least 30% margin.
  • Core loss is not modeled — ferrite and laminated iron cores have frequency-dependent losses. The dissipation value applies only to the resistive element.
  • Stray capacitance is not modeled — all real inductors have parasitic shunt capacitance that causes self-resonance. The first-order RL model is valid well below the self-resonance frequency.
  • The back-EMF estimate is screening only — V ≈ L·I/Δt assumes constant di/dt during switching. Real peaks are bounded by stray capacitance, switch breakdown, arc formation, and any clamp device.
  • De-energize freewheel loop resistance is assumed equal to R — real freewheel paths include diode forward drops, Zener clamp voltages, or RC snubber dynamics that change the decay shape.
  • Mutual coupling not modeled — coupled inductors (transformers, common-mode chokes) require coupled circuit equations.
  • AC sources are out of scope — the calculator assumes DC supply. AC analysis requires impedance methods.
  • Switching-converter inductor design is out of scope — τ gives intuition but does not size inductors for buck, boost, or buck-boost converters.
  • Functional safety for brakes is not verified — brake-coil application context is educational only. Safety-rated brake design must follow IEC 60204-1, ISO 13849-1, or equivalent.

Common Mistakes to Avoid

  • Forgetting the inductor DCR when entering resistance — the coil's own winding resistance is always part of R. Neglecting DCR makes τ larger and I_ss higher than reality.
  • Entering inductance in the wrong unit (e.g. mH when μH was intended) — produces a 1000× wrong τ. Always verify the unit dropdown matches the datasheet value.
  • Assuming higher supply voltage means faster response — it increases I_ss and stored energy, but τ = L/R is unchanged.
  • Confusing 5τ settling time with relay pickup time — τ governs electrical current rise, not the mechanical armature movement. Consult the relay datasheet for specified pickup time.
  • Sharing one resistor across parallel inductive loads — current imbalance builds up unpredictably. Use individual resistors or constant-current drivers per load.
  • Omitting a flyback diode when driving an inductive load from a MOSFET or BJT — back-EMF transients reliably destroy the switch within hundreds to thousands of switching cycles.
  • Treating the back-EMF screening estimate as the actual measured peak — the real peak is bounded by stray capacitance and switch breakdown, usually much lower than L·I/Δt predicts.
  • Using AC RMS voltage as the supply input — use the DC value at the inductor terminals after rectification.

Frequently Asked Questions

What is the RL time constant and how do I calculate it?
The time constant of a series RL circuit is τ = L/R, where L is the inductance in henries and R is the total series resistance in ohms. The result has units of seconds. To calculate: divide L by R with consistent units. Example: a 200 mH coil with 400 Ω winding resistance gives τ = 0.200 / 400 = 500 μs. After one time constant, current in an energizing RL circuit reaches 63.2% of its final value (V/R). After five time constants, current reaches 99.3% — the conventional engineering threshold for "fully settled." For precision applications, after 7τ the remaining error is 0.09%.
Why is the RL time constant L divided by R?
The differential equation for a series RL circuit is L·di/dt + i·R = V. The exponential solution contains e^(−t·R/L) — the ratio R/L appears in the exponent. Its reciprocal L/R has units of time and serves as the characteristic time scale of the circuit. The grouping is dictated by the math, not chosen by convention.
How do I find the time constant from a circuit schematic?
Identify the inductor's value L and add up all series resistances: the inductor's own DC winding resistance (DCR from the datasheet), any external resistors, wire and trace resistance (often negligible), and the on-resistance of any switching element. Divide L by this total R.
How do I reduce the time constant of an RL circuit?
Either decrease L or increase R. Increasing R is the easier path in most designs (swap a series resistor) but reduces steady-state current V/R, which may affect relay pickup or solenoid holding force. Decreasing L means swapping the inductor for a smaller value, which is harder once the part is selected. The Design Verification mode shows the exact L or R you need to hit a target τ.
Does supply voltage affect the RL time constant?
No. τ = L/R depends only on inductance and resistance. Supply voltage changes the steady-state current I_ss = V/R and the energy stored W = ½·L·I², but does not change τ. A common student misconception is that higher voltage means faster response — what actually happens is that the same exponential curve reaches the pickup-current threshold sooner because I_ss is larger.
Why does a flyback diode slow relay release?
A flyback diode clamps the inductor's de-energize voltage to its small forward drop (about 0.7 V for silicon). With only this low voltage driving the discharge, current decays slowly through the freewheel loop, and the armature takes longer to release. A Zener-clamped flyback or TVS allows higher clamp voltage (typically 20–40 V), which forces faster di/dt and faster release — at the cost of higher voltage stress on the switching element.
Can back-EMF damage a MOSFET or microcontroller pin?
Back-EMF (back electromotive force) is the voltage an inductor generates in opposition to a change in current: V_L = −L·di/dt. During abrupt switch opening, the inductor drives a large reverse-polarity spike to sustain the current that was flowing. Yes, this spike reliably damages unprotected semiconductors. Logic-level MOSFETs commonly have a 20–30 V Vds breakdown rating; microcontroller GPIO pins clamp at about 5.7 V on a 5 V system. Inductive back-EMF without a flyback diode reliably exceeds both. Cumulative avalanche stress destroys the switch within hundreds to thousands of cycles. Always include a flyback diode, TVS, or other clamp when driving inductive loads from semiconductors.
What is the difference between the RL time constant and relay pickup time?
The RL time constant τ = L/R describes how quickly current in the coil approaches its steady-state value V/R — it is a purely electrical quantity. Relay pickup time is the time until the contacts actually close, which is always longer than τ because the armature has mass and inertia, and the magnetic force must overcome the return spring before mechanical movement begins. A relay with τ = 2 ms may have a specified pickup time of 8–15 ms. Always consult the relay datasheet for the pickup time; τ cannot substitute for it.

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