Magnetic energy in an RL circuit

A coil resists sudden current changes

An inductor is a coil that stores energy in a magnetic field and opposes changes in current; L denotes its inductance. RL means Resistor Inductor, a resistor–inductor circuit. A millihenry (mH) is one thousandth of a henry, a millisecond (ms) one thousandth of a second and a millijoule (mJ) one thousandth of a joule of energy.

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EXPERIMENT BENCH

Change the circuit settings, predict the readings, then check a challenge. These are learning models, with the assumptions explained in each lesson.

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Why it works

Ideal initially unenergized coil after a voltage step. Elapsed time is a chosen sample, not a live clock; winding resistance, magnetic saturation and switch-off voltage spikes are omitted.

Vs is applied voltage, R series resistance, L inductance and t time since switching on. τ = L/R; I(t) = Vs/R × (1 − exp(−t/τ)); exp is the exponential function. Coil voltage = Vs × exp(−t/τ); stored energy E = ½LI².

Difficulty

Build · Build it
Power on at 5 V, 100 Ω, 100 mH and 1 ms. Read about 31.606 mA.
Need a hint?
Vs = 5 V; R = 100 Ω; L = 100 mH; t = 1 ms → 31.606 mA
Explore · Change one thing
At 5 V, 100 Ω and 100 mH, choose a time giving at least 49 mA and coil voltage at most 0.1 V.
Need a hint?
Vs = 5 V; R = 100 Ω; L = 100 mH; t = 4 ms → 49.084 mA; 0.092 V
Solve it · Solve the challenge
At 5 V, 50 Ω and 200 mH, choose a time giving 62–64 mA and stored energy 0.38–0.42 mJ.
Need a hint?
Vs = 5 V; R = 50 Ω; L = 200 mH; t = 4 ms → 63.212 mA; 0.400 mJ

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