RL Time Constant

The RL time constant tells you how quickly current changes in a resistor-inductor circuit after a switch is opened or closed. It comes from the fact that an inductor opposes changes in current through the induced voltage it creates, while the resistor limits how fast current can build up or die away; the ratio L/R sets the timescale of that exponential change. After one time constant, the current has reached about 63% of its final value when rising, or fallen to about 37% of its original value when decaying.

Use this formula when analyzing transient behavior in circuits that contain both inductors and resistors, especially right after a switching event. It is common in electromagnetics, circuit design, and any problem asking how long an RL circuit takes to respond.

• Using millihenries and ohms without converting inductance to henries first
• Confusing the RL time constant with the RC time constant formula
• Thinking the time constant is the total settling time instead of the characteristic exponential timescale