Inductance & RL Circuits
RL circuit — current ramp. Builds on Faraday's Law and Batteries & EMF.
You build a simple circuit: a battery, a switch, a resistor, and an inductor (a coil of wire) all in series. The inductor has a large inductance L. You close the switch at t = 0.
What happens to the current immediately after closing the switch?
The current rises gradually! An inductor opposes changes in current by generating a back-EMF. At t = 0, the inductor acts like an open circuit (zero current). Over time, the current grows exponentially: I(t) = (V/R)(1 − e^(−t/τ)), where τ = L/R is the time constant. After about 5τ, the current has essentially reached its maximum value V/R.
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Close and open the switch to see the current rise and decay exponentially. Watch how the inductor voltage spikes when the switch opens — this is the back-EMF that can create sparks!
I(t) = (V/R)(1 − e^(−t/τ))
After one time constant τ, the current reaches 63% of its final value. After 5τ, it’s at 99.3%. The inductor is the electrical analog of mass — it resists changes in current just as mass resists changes in velocity.
Your car’s spark plugs use an inductor. When the circuit is broken, the inductor’s back-EMF creates a voltage spike of 20,000–40,000 volts — enough to arc across the spark plug gap and ignite fuel.
The inductor (ballast) in a fluorescent lamp limits the current through the gas tube and provides the initial voltage spike needed to ionize the gas and start the lamp.
Inductors in speaker crossovers act as low-pass filters, blocking high-frequency signals to the woofer. The RL time constant sets the cutoff frequency.
Large inductors protect power grids from sudden current surges (like lightning strikes) by slowing the rate of current change, giving circuit breakers time to react.
“An inductor is electrical inertia. It says: “You can’t change my current instantly.” Try, and it fights back with voltage. That voltage spike from a tiny coil can create a 40,000-volt spark — enough to ignite gasoline.”
RL Circuit Lab
Build your own RL circuit by adjusting the inductance and resistance. Toggle the switch on and off to see the current rise and decay. Watch the I(t) and V_L(t) graphs build up in real time.
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Start with L = 1 H and R = 10 Ω. Close the switch and watch the current rise to V/R. Now double L to 2 H — the rise is twice as slow (τ doubles). Try halving R instead — the final current doubles AND the rise time doubles. Open the switch suddenly and watch the inductor voltage spike!
The time constant τ = L/R controls everything. Large L means slow response (lots of electrical inertia). Small R means slow response too (less energy dissipation). The inductor’s back-EMF at switch-off can far exceed the battery voltage — that’s how a 12V car battery creates a 40,000V spark.