Calculation
i(t) = (U/R)·[1−exp(−R·t/L)]
After time constant τ=L/R, current reaches about 63.2% of its steady value U/R.
Dubbel Elektrotechnik, Einschalten einer ohmsch-induktiven Last
RL coil current rise
After time constant τ=L/R, current reaches about 63.2% of its steady value U/R.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Coil current i(t) — Current in the RL branch at the selected time after switching.
- Applied DC step U — Constant DC voltage applied at t=0 to the initially current-free RL branch.
- Total resistance R — Sum of coil winding, series resistor, wiring and relevant source resistance.
- Inductance L — Effective coil inductance over the considered current range without saturation.
- Time since switching t — Elapsed time from the idealised voltage step at t=0.
Example
U=24 V, R=6 Ω, L=120 mH and t=40 ms give τ=20 ms, I∞=4 A and i≈3.46 A.
Assumptions and limits
Zero initial current, ideal constant DC and constant linear inductance; core saturation, flyback path and switching overvoltage are excluded.
Understand RL coil current rise
This calculator shows how quickly coil current rises after applying DC, linking steady current U/R to electromagnetic time constant L/R.
What does this quantity describe?
Inductor current cannot jump. From L·di/dt+R·i=U follows i=(U/R)(1−e^(−t/τ)), τ=L/R. After τ current reaches 63.2%; after about 5τ it exceeds 99%.
Formula and variables
i(t) = (U/R)·[1−exp(−R·t/L)]
τ = L/RI∞ = U/Ri(t) = I∞·(1−e^(−t/τ))
| Symbol / input | Meaning |
|---|---|
| Coil current i(t) | Current in the RL branch at the selected time after switching. |
| Applied DC step U | Constant DC voltage applied at t=0 to the initially current-free RL branch. |
| Total resistance R | Sum of coil winding, series resistor, wiring and relevant source resistance. |
| Inductance L | Effective coil inductance over the considered current range without saturation. |
| Time since switching t | Elapsed time from the idealised voltage step at t=0. |
Choose the inputs correctly
U is constant post-switch voltage. R includes winding, series, wiring and relevant source resistance. L is effective inductance over the current range, and t starts from an initially current-free branch.
How to use the calculator
Determine R at the temperature relevant to the question, obtain L from data or measurement, and enter available energising time. Check both current and U/R against switch and coil ratings.
Worked example
24 V, 6 Ω and 120 mH give τ=20 ms and I∞=4 A. After 40 ms=2τ, current is about 3.46 A.
Understand the result and units
Greater inductance slows rise but does not change final current at fixed R. Greater resistance lowers final current and shortens τ.
Use V, Ω, H/mH/µH and ms/s; internally τ=L/R is seconds and I is amperes.
Typical applications
Solenoid valves, relays, DC chokes, actuators and first-order switching labs.
Assumptions, limits and common mistakes
Constant linear inductance and ideal DC source. Saturation, moving armature, winding temperature, PWM, flyback path and turn-off overvoltage are excluded.
Common mistake: Using only an external resistor instead of total series resistance corrupts both final current and time constant. Turn-off may also use a different circuit.
Frequently asked questions
What is “RL coil current rise” used for?
Solenoid valves, relays, DC chokes, actuators and first-order switching labs.
Where do the input values come from?
U is constant post-switch voltage. R includes winding, series, wiring and relevant source resistance. L is effective inductance over the current range, and t starts from an initially current-free branch.
What does the result not cover?
Constant linear inductance and ideal DC source. Saturation, moving armature, winding temperature, PWM, flyback path and turn-off overvoltage are excluded.