RL Circuit: Self-Inductance & Current Transients (2D)

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

Inductor voltage V_L

0.00 V

Energy U = ½LI²

0.00 J

I(t) — last 8 s

V_L(t) = L·dI/dt — 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
Kirchhoff loop (switch open):    0 = I·R + L·dI/dt
This engine integrates dI/dt = (V_target − I·R)/L
numerically every frame (RK4 sub-steps), it does not
just evaluate the closed-form exponential.
Closed form (for comparison):
  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 field-line density around the coil and the moving charge markers respond in real time.
Field lines around the inductor scale with |I|/I_max — this is the magnetic field of the coil, 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 lines