Self-Induction

Interactive simulation of self-induction in RL circuits - explore current growth, decay, back EMF, and magnetic field changes

Circuit Visualization

Current: 0.00 mA
Inductance: 5.0 H
Back EMF: 0.00 V
Time Constant: 0.50 s
Time: 0.00 s
Magnetic Flux: 0.00 mWb

Circuit Parameters

Component Values

Animation Controls

Display Options

Self-Induction Equations

Back EMF: ε = -L·(dI/dt)
Current Growth: I(t) = (V₀/R)·(1 - e^(-t/τ))
Current Decay: I(t) = I₀·e^(-t/τ)
Time Constant: τ = L/R
Magnetic Flux: Φ = L·I
Magnetic Energy: E = ½LI²
Current Parameters: τ = 0.50 s, I₀ = 1.00 A, E_max = 2.50 J

Instructions

  • Click "Close Switch" to connect the circuit and observe current growth
  • Click "Open Switch" to disconnect and observe current decay
  • Observe how the inductor opposes current changes (Lenz's Law)
  • The time constant τ = L/R determines the speed of current change
  • After 5τ, the current reaches 99.3% of its final value
  • Compare with a circuit without inductor to see the difference

What is Self-Induction?

Self-induction is a phenomenon where a changing current in a circuit induces an electromotive force (EMF) in the same circuit. According to Faraday's law, any change in magnetic flux through a circuit induces an EMF, and according to Lenz's law, this induced EMF always opposes the change that produced it. In an inductor, the magnetic field generated by the current links back to the circuit itself, creating this self-induced EMF (back EMF).

Closing the Switch (Current Growth)

When the switch closes, current begins to flow through the circuit. However, the inductor immediately generates a back EMF ε = -L·(dI/dt) that opposes the increase in current. As a result, the current grows exponentially according to I(t) = (V₀/R)·(1 - e^(-t/τ)), where τ = L/R is the time constant. Initially, the inductor acts like an open circuit, and the current is zero. Over time, as the rate of current change decreases, the back EMF decreases, and the current approaches its final value I₀ = V₀/R.

Opening the Switch (Current Decay)

When the switch opens, the power source is disconnected, but the inductor maintains current flow by converting its stored magnetic energy back into electrical energy. The back EMF now opposes the decrease in current, causing the current to decay exponentially according to I(t) = I₀·e^(-t/τ). The inductor acts as a temporary energy source, releasing the energy stored in its magnetic field (E = ½LI²) back into the circuit.

Time Constant

The time constant τ = L/R is the characteristic time scale of an RL circuit. A larger inductance L means a stronger opposition to current changes (more energy storage), resulting in a longer time constant. A larger resistance R means faster energy dissipation, resulting in a shorter time constant. At t = τ, the current has changed by 63.2% of the total change. At t = 5τ, the transient is 99.3% complete and considered finished for most practical purposes.

Magnetic Field and Energy

When current flows through an inductor, it creates a magnetic field. The magnetic flux Φ through the inductor is proportional to the current: Φ = L·I. This magnetic field stores energy with density proportional to the square of the magnetic field strength. The total stored energy is E = ½LI², which is the work done against the back EMF to establish the current.

Applications

Self-induction has numerous practical applications: transformers for voltage conversion; inductors in filters and tuning circuits; electric motors and generators; relays and solenoids; energy storage in switch-mode power supplies; ignition systems in combustion engines; wireless charging systems; and inductive sensors.