Inductor & RL Circuit Back EN · ZH
Circuit Simulator

Inductor & RL Circuit Transient Response

Visualize I(t) and V_L(t) in real time for energizing, de-energizing, and AC steady-state modes. Automatically calculates time constant τ, energy storage, reactance, impedance, and phasor diagram.

Parameters
Mode
Inductance L 10.0 mH
Range: 1 μH – 100 H (log)
Resistance R 100 Ω
Range: 0.01 Ω – 100 kΩ (log)
Supply Voltage V₀ 12.0 V
Initial Current I₀ 0.00 A
Time Constant τ
I(τ) [A]
Energy ½LI² [J]
X_L / |Z| [Ω]
Current I(t) Transient Response
Inductor Voltage V_L(t)

Theory

Energizing: $I(t) = \dfrac{V_0}{R}\!\left(1 - e^{-t/\tau}\right) + I_0\,e^{-t/\tau}$, $\tau = \dfrac{L}{R}$

De-energizing: $I(t) = I_0\,e^{-t/\tau}$, $V_L(t) = -R\,I_0\,e^{-t/\tau}$

Energy: $U = \dfrac{1}{2}LI^2$

AC: $X_L = \omega L = 2\pi f L$, $|Z| = \sqrt{R^2 + X_L^2}$, $\phi = \arctan\!\left(\dfrac{X_L}{R}\right)$

Applications: RL circuit analysis is directly applicable to motor winding design, transformer modeling, and solenoid valve transient current. Use for snubber coil optimization, EMI filter design, and circuit-level pre-checks before full electromagnetic FEA.