Self-inductance – RL circuit and time constant τ = L/R
PhysicsElectric & Magnetic FieldsAges 17–18Virtual lab
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Build a solenoid (turns, length, radius, iron core) to get L = μ₀μᵣN²A/l, then switch an RL circuit on and off: the current grows and decays exponentially with τ = L/R, the back emf is −L·di/dt and the coil stores ½LI²; a lamp lights late at switch-on and flashes at switch-off. Further screens measure L with a triangular current, show mutual induction with and without an iron core, and compare the coil's DC resistance with its AC impedance.
Lesson: Self-inductance, RL circuits and mutual induction
What it shows
When the current in a coil changes, the coil's own magnetic flux changes and induces an emf ε = −L·di/dt that opposes the change (Lenz's law). For a long solenoid L = μ₀μᵣN²A/l, so more turns or an iron core give a much larger inductance. In a circuit with resistance R the current cannot jump: it rises as I = (ε/R)(1 − e^(−t/τ)) and decays as I₀e^(−t/τ), with time constant τ = L/R, and the coil stores energy ½LI². The model treats the coil as an ideal solenoid in series with its wire resistance r, the lamps as fixed resistors and the diode as ideal.
How to use
Press Close K or tap the switch: the current and the 63 % mark appear in slow motion, and the measured τ goes into the Results table. Choose a circuit with lamps to see a lamp light late or flash. On Triangular current, record the coil voltage and |di/dt|; on Mutual induction, compare Air and Iron core; on DC / AC, record V and I for both supplies. Untick Show theoretical values (L, τ, M, Z) and answer each task.
Parameters you can change
- Screen Switching an RL circuit, Triangular current, Mutual induction, DC and AC
- Number of turns N 100–2000
- Coil length l 5–50 cm
- Coil radius 0.5–4 cm
- Core Air, Iron
- Relative permeability μᵣ of the iron core 10–2000
- Coil resistance r 1–50 Ω
- Supply emf ε (supply voltage V on the DC/AC screen) 1–12 V
- Resistance R 1–200 Ω
- Circuit (switching screen) R in series with the coil, diode for switch-off, Two lamps: the lamp with the coil lights late, Lamp across the coil: flashes at switch-off
- Secondary turns N₂ (mutual induction) 100–2000
- How the primary current changes (mutual induction) Switch K on/off, Steady rise or fall over 0.5 s
- Triangular current frequency 5–1000 Hz
- Triangular current amplitude Iₘ 1–100 mA
- AC frequency 10–1000 Hz
- Show theoretical values (L, τ, M, Z)
Questions to explore
- How does doubling the number of turns change the inductance L and the time constant τ?
- Why does a lamp connected across a coil flash when the switch is opened?
- Why does an iron-cored coil pass much less alternating current than direct current?
