RL Time Constant Calculator
Time constant (ms)
0.1
How it works
The RL time constant (τ = L / R) defines how quickly current builds or decays in an inductor-resistor circuit. At time τ, current reaches 63.2% of its final value. After 5τ, current is essentially at steady state.
**Current behavior** When voltage is applied: I(t) = (V/R) × (1 - e^(-Rt/L)). The steady-state current is V/R (the inductor acts as a short circuit at DC after full current is established). When voltage is removed, current decays: I(t) = I_0 × e^(-Rt/L). Unlike capacitors (which maintain voltage), inductors maintain current.
**Inductive kick and flyback** When current through an inductor is suddenly interrupted (switch opens), the inductor attempts to maintain current — it generates a large voltage spike: V = L × (dI/dt). For fast switching, this can produce hundreds or thousands of volts. Flyback diodes (placed in reverse across the inductor) clamp this spike by providing a current path. Essential protection for relay coils, motor windings, and solenoids.
**RL filters** An RL circuit forms a first-order filter. Low-pass: take output across the resistor for high frequencies (inductor blocks them). High-pass: take output across the inductor. Cutoff frequency: f_c = R / (2πL). RL filters are less common than RC because inductors are bulkier and more expensive, but RL is preferred at high power levels where large capacitors would be impractical.
**Motor winding and time constant** Electric motors have RL characteristics from winding resistance and inductance. The mechanical time constant (angular velocity rise) differs from the electrical time constant (current rise). Understanding both is necessary for servo and drive system control design.
Frequently Asked Questions
- For a buck converter: L = (V_in - V_out) × D / (f_sw × ΔI_L), where D = V_out/V_in (duty cycle), f_sw is switching frequency, and ΔI_L is peak-to-peak ripple current (typically 20–40% of rated output current). Example: 12V to 5V, 3A output, 500 kHz, 30% ripple: D = 5/12 = 0.417. L = (12-5) × 0.417 / (500,000 × 0.9) = 6.5 µH. Saturation current rating must exceed peak current: I_peak = I_avg + ΔI/2 = 3 + 0.45 = 3.45 A. The RL time constant here is not the primary design parameter — saturation current and core losses are.
- When a switch (transistor, relay, MOSFET) controlling an inductive load (motor, solenoid, relay coil) opens, the inductor generates V = L × dI/dt. With fast switching (dI/dt is large), this voltage spike can be hundreds of volts — far exceeding the switch's breakdown voltage. A flyback diode (also called freewheeling or snubber diode) is placed in reverse across the load: when the switch opens, inductor current flows through the diode, clamping the voltage to one diode drop above supply. Without it: switch destroys itself within microseconds. Always include flyback diodes when controlling inductive loads from digital outputs.
- When a DC motor is first connected, back-EMF is zero (shaft not yet spinning). Starting current = V_supply / R_winding, which can be 5–10× rated running current. The RL time constant determines how quickly this current rises: I(t) = (V/R) × (1 - e^(-t/τ)). A motor with L = 10 mH, R = 1Ω: τ = 10 ms. Full current (rated) is reached in ~50 ms. This high inrush: causes voltage sag on the supply, trips overcurrent protection, and creates mechanical shock. Mitigation: soft starters (gradually increase voltage), star-delta starting (reduce voltage 57%), VFDs (control acceleration ramp), or current-limiting resistors switched out as speed increases.
- MOSFET gate has capacitance (~nF range). Gate drive current charges this capacitance through the gate drive resistor, creating an RC time constant (not RL). However, the load inductance interacts with switching speed: faster switching (high dV/dt and dI/dt) causes: oscillation with stray inductance in gate drive loop, EMI from rapid current changes, and voltage spikes on the drain exceeding VDS max. Slower gate resistance reduces these problems but increases switching losses. Optimal gate resistance balances switching speed, EMI, overshoot, and thermal performance — typically found by experiment or simulation, often starting with 10–47Ω and adjusting.