What is the RL time constant?

The time constant τ = L/R (in seconds) is the time it takes for the current in a series RL circuit to reach approximately 63.2% of its final steady-state value after a step voltage is applied. After 5τ the circuit is considered fully settled (>99%).

How is impedance different from resistance?

Resistance R opposes DC and AC current equally. Inductive reactance X_L = 2πfL opposes only AC current, and it increases with frequency. Total impedance Z = √(R² + X_L²) combines both effects and is used for AC analysis.

Why does current lag voltage in an RL circuit?

An inductor resists changes in current (back-EMF). This causes the current to build up more slowly than the applied voltage, resulting in the current lagging the voltage by a phase angle φ = arctan(X_L / R), ranging from 0° (pure resistive) to 90° (pure inductive).

What is the cutoff frequency of a series RL circuit?

When used as a low-pass filter (output taken across R), the −3 dB cutoff frequency is f_c = R / (2πL). This equals 1/(2πτ) and is the point where output power drops to half and the phase shift is exactly 45°.

What units should I use?

Use consistent SI units: ohms (Ω) for resistance, henries (H) for inductance, and hertz (Hz) for frequency. The calculator accepts millihenries (mH) and microhenries (μH) via the unit selector and converts automatically.

RL Circuit Calculator

Enter resistance and inductance to compute the RL time constant, impedance, phase angle, and transient voltage/current response.

Circuit Parameters

Resistance (R)

Inductance (L)

AC Frequency (Hz) (optional)

Supply Voltage (V) (for transient chart)

Quick Presets

Time Constant τ

—

τ = L / R

Cutoff Frequency f_c

—

f_c = R / (2πL)

Reactance X_L

—

X_L = 2πfL

Impedance Z

—

Z = √(R² + X_L²)

Phase Angle φ

—

φ = arctan(X_L / R)

Steady-State Current

—

I_ss = V / R

Transient Response — Current at nτ

Time	I(t) (A)	% of I_ss

Current Transient Response I(t)

I(t) = I_ss × (1 − e^−t/τ)

Summary

A series RL circuit combines a resistor (R) and an inductor (L) in series. This calculator derives the time constant τ = L/R, which governs how quickly current rises to its steady-state value. It also computes AC impedance Z = √(R² + (ωL)²) and phase angle φ = arctan(ωL/R) at any frequency you specify.

How it works

Enter the resistance R in ohms and inductance L in henries (or use the unit selectors for kΩ, mH, μH).
Optionally enter an AC frequency in Hz to compute impedance and phase angle.
The calculator derives the time constant τ = L/R — the time for current to reach ~63.2% of its final value.
Inductive reactance X_L = 2πfL and total impedance Z = √(R² + X_L²) are computed from the frequency.
Phase angle φ = arctan(X_L / R) tells you how much the current lags the voltage.
The transient response chart plots current I(t) = V/R × (1 − e^(−t/τ)) over five time constants.

Use cases

Design low-pass RL filters and verify the −3 dB cutoff frequency.
Estimate inrush current rise time in motor and solenoid driver circuits.
Analyze transient behavior in switching power supplies.
Verify inductor selection for a given settling time requirement.
Calculate impedance matching for audio crossover networks.
Troubleshoot phase shift in AC power factor correction circuits.
Teach or learn RL circuit theory with an interactive visual aid.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu