RL Time Constant Calculator

The RL time constant determines how quickly current builds up or decays in an inductive circuit. After one time constant, current reaches 63.2% of its final value.

📡 Circuits📐 τ = L/R⚡ Inductance

Inductance L (H)

Resistance R (Ω)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Time Constant	τ	τ = L/R	s
Inductance	L	L = τR	H
Resistance	R	R = L/τ	Ω
Current at t	I(t)	I_max(1 − e^−t/τ)	A
5 time constants	5τ	~99.3% of final value	s

Step-by-Step Examples

Example 1

Relay Coil

Relay: L = 50 mH, R = 200 ohm.

tau = L/R = 0.05/200 = 0.25 ms
5*tau = 1.25 ms to reach steady state

✓ 0.25 ms time constant

Example 2

Motor Winding

DC motor: L = 10 mH, R = 2 ohm.

tau = 0.01/2 = 5 ms
Current reaches 63.2% in 5 ms

✓ 5 ms — slow compared to relay

Example 3

Power Inductor

Inductor L = 1 mH, R = 0.1 ohm.

tau = 0.001/0.1 = 10 ms
Cut-off frequency = R/2*pi*L = 15.9 Hz

✓ 10 ms time constant

Real-World Applications

⚡

Relay Controls

RL time constant determines relay switching speed and snubber circuit design.

🚗

DC Motors

Motor winding inductance creates current lag on startup and speed changes.

📡

Power Electronics

Inductor current cannot change instantaneously — RL tau governs boost/buck converter dynamics.

🔊

Audio Crossovers

RL circuits form low-pass filters directing bass frequencies to woofers.

Common Mistakes to Avoid

⚠️

Confusing with RC

RL: tau = L/R. RC: tau = R*C. Both have units of seconds. RL time constant decreases with R (opposite to RC behavior in terms of which element type increases tau).

⚠️

Forgetting steady-state time

Steady state is reached after about 5*tau. During transient, voltage and current change exponentially.

⚠️

Neglecting inductor resistance

Real inductors have DC resistance (DCR). Include DCR in total R for accurate tau.

Frequently Asked Questions

Why is tau = L/R? ▾

From the RL differential equation: L*dI/dt + R*I = V. Solution is I(t) = V/R*(1-e^(-t*tau)) where tau = L/R.

What happens at one time constant? ▾

I = I_max*(1-e^-1) = 0.632*I_max. After 5*tau, I = 0.993*I_max (effectively at steady state).

How does RL compare to RC? ▾

Both have exponential responses with tau. RL: current builds up. RC: voltage builds up. Both reach ~99% in 5*tau.

Can you have negative time constant? ▾

No — negative tau would mean exponentially growing response, which is unstable. All passive RL circuits have positive tau.

How does RL circuit filter frequencies? ▾

RL is a low-pass filter with cutoff f_c = R/(2*pi*L). Frequencies above f_c are attenuated by the inductor impedance.

Related Physics Calculators

Formula Explorer connections

Interpretation: This formula links charge, voltage, current, resistance, capacitance, power or circuit time response. Assumption: Confirm DC versus AC conditions, RMS versus peak values, component topology and steady-state versus transient behavior. Ideal components may be assumed.

Thévenin & Norton Equivalent Calculator →Transformer Turns Ratio Calculator →Voltage Divider Calculator →Physics Formula Explorer →