RL Circuit: Self-Inductance & Current Transients

Circuit

Voltage V 12.0 V

Resistance R 10.0 Ω

Inductance L 1.00 H

Live Readouts

Current I

0.00 A

Time constant τ = L/R

0.100 s

Energy stored U = ½LI²

0.00 J

I(t) — last 8 s

How it works

A resistor and a coil (inductor) in series with a battery and a switch form an RL circuit. The coil resists any change in current because a changing current changes its own magnetic flux, inducing a back-EMF (Faraday's law / Lenz's law) that opposes the change — this is self-inductance.

Kirchhoff loop (switch closed):  V = I·R + L·dI/dt
Charging:   I(t) = (V/R)·(1 − e^(−tR/L))
Discharging: I(t) = I₀·e^(−tR/L)
Time constant: τ = L/R
Energy stored in the field: U = ½LI²

Switch — closed connects the battery: current climbs toward the steady-state value V/R. Open removes the battery: the coil's collapsing field drives the existing current back down through R until it reaches zero.
V, R, L sliders — change the target current (V/R) and the time constant (τ = L/R) live; the solenoid's rendered field and the wire's moving charge markers respond in real time.
Field arrows inside the coil scale with |I|/I_max — this is the magnetic field B ≈ μ₀nI of a long solenoid, growing as the current rises and collapsing as it decays.
Real-world relevance: this exact transient governs relay coils, motor windings, transformer inrush, and why switching off an inductive load (a motor, a solenoid valve) can produce a damaging voltage spike unless a flyback diode is used.

CLOSED — charging

Moving charge (current) Magnetic field (B)

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