Capacitance and inductance
RL time constant
- where
- time constant (s)
- inductance (H)
- resistance (Ω)
Explain this equation
Works out the time constant of a resistor–inductor circuit. Sets how quickly current builds up or dies away in a coil.
τ is the time constant in seconds. L is the inductance in henries. R is the total series resistance, including the coil’s own winding resistance.
Inductance resists changes in current, so more L slows things down. More resistance lowers the final current, so it is reached sooner. Hence L divided by R.
Sense check: 0.1 H with 10 Ω gives 0.01 s. After one τ the current reaches about 63% of its final value; after about 5τ it is treated as settled.
Watch out: it is L ÷ R, not L × R as with the RC formula.
Current in a first-order RL circuit changes gradually. Divide inductance by the total series resistance to find the time constant.
Include coil resistance in the total. The relationship describes the transient pace, not the final DC current.
Enter your values to see the result.
Common mistake
Multiplying L by R by analogy with RC.
Limits
Linear inductor and fixed resistance.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.