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LR circuit growth and decay
Intermediate
Current rises exponentially with time constant L/R.
τ = L/RCurrent in an LR circuit rises as I = (V/R)(1 − e^{−Rt/L}) and decays as I₀e^{−Rt/L}, time constant τ = L/R.
L = 0.1 H, R = 10 Ω: τ = 10 ms.
Analogous to RC.
In more detail
In an LR circuit, current rises exponentially towards V/R when the voltage is applied, with time constant L/R. When the source is removed, the current decays exponentially.
Real-world uses
- Relays and solenoids respond with delays set by their inductance.
- Circuit analysis of inductors uses the LR time constant.
- Engineers designing relays and solenoid valves consider how fast the current builds up in an inductor.
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Frequently asked questions
What is the time constant?
L divided by R, the time for current to reach about 63% of its final value.
Why does the current not jump?
Because the inductor opposes sudden changes in current.
What is the time constant of an LR circuit?
L divided by R, which is the time for the current to reach about 63 percent of its final value.
Related topics in Magnetism & Induction
AC generator · Dynamo and alternator · Back emf in a motor · Maxwell's displacement current · Maxwell's equations · Magnetic monopoles