RL Time Constant

Formula

Description

The RL time constant describes how quickly current builds up or decays in an inductive circuit. After one time constant, the current reaches 63.2% of its final value when energizing, or drops to 36.8% when de-energizing. Notice that unlike the RC circuit where τ = RC, the RL time constant has inductance in the numerator and resistance in the denominator. Higher inductance means slower current changes (more energy stored in the magnetic field), while higher resistance means faster current changes (more energy dissipated per cycle).

Variables

• τ — Time constant in seconds (s)
• L — Inductance in henries (H)
• R — Resistance in ohms (Ω)

Practical Notes

The RL time constant is critical in relay and solenoid driver design. When current through an inductor is suddenly interrupted, the collapsing magnetic field generates a large voltage spike (back-EMF) that can damage switches and transistors. Flyback diodes are used to safely dissipate this stored energy.