Generators: turning motion into electricity: sources & model

Turn a tabletop generator, unplug its lamp, and replay the same motion. Follow the voltage, the pushback and every joule to discover where electrical energy comes from.

What supports the explanation?

What this model assumes

1. Prescribed steady motion and a uniform imposed field omit acceleration energy, self-inductance, switching transients, armature reaction, saturation, core loss, friction and changing resistance. Load/speed changes initialize a new steady comparison.
2. The apparent lamp is a fixed resistor with illustrative glow, not a calibrated incandescent lamp or an LED circuit. Real crank lights may also have gears, rectifiers, regulators and storage.
3. Calculated traces and motion are not experimental measurements. Replay time may be slowed for viewing; model time is labeled separately.
4. The original geometry represents 100 equal-area turns with a visible bundle. It is not a scan, manufacturer model or museum replica.
5. The paper investigation determines interval-mean voltage, not an exact instantaneous waveform or exact load energy.
6. Define the signs before drawing arrows: The shaft is +z; B points along +x. The positive coil normal is n=(cosθ,sinθ,0). Positive winding circulation follows the right-hand rule about n; terminal labels stay fixed. Positive external conventional current travels A → load → B. Animated cues show direction, not individual electron speed.
7. Flux linkage and its slope: For N equal turns, each of area A, λ=NBA cosθ. Set K=NBA. At prescribed steady angular velocity ω, θ=θ₀+ωt and e=−dλ/dt=Kω sinθ. Face-on flux can be largest while its slope is zero. Edge-on flux can be zero while its slope is largest. A stationary coil can also have emf in a changing external field; this workbench holds that field fixed.
8. Chosen numbers, not a measured machine: This original calculation uses N=100, A=0.0100 m² per turn, B=0.200 T and K=0.200 Wb-turn. Winding/contact resistance Rc=2 Ω; loads are open, 8 Ω or 2 Ω. Speeds are rest, ±10 or ±20 rad/s. These are authored parameters, not dimensions or measurements extracted from museum photographs.
9. Voltage inside and outside: For a connected resistive load, signed i=e/(Rc+RL). Terminal voltage Ut=iRL=e−iRc. At θ=90°, ω=10 rad/s and RL=8 Ω, generated emf is +2 V, current +0.2 A and terminal voltage +1.6 V. With the plug out, i=0 and Ut=e; an open circuit has no delivered load power. Real unloaded machines still have losses omitted here.
10. A torque and energy check: The rotor’s electromagnetic torque is τem=−Ki sinθ; the required electromagnetic driving torque is −τem. Thus Pinput=−τemω=ei=i²RL+i²Rc. Reversing ω reverses current and torque at the same θ; τem still opposes motion. The resistive load does not return energy just because current has a negative sign.
11. A full revolution: At +10 rad/s, a full turn takes 2π/10≈0.6283 s, about 95.49 rpm. For the 8 Ω load, mean input/load/heating powers are 0.20/0.16/0.04 W. Full-turn energies are about 0.12566/0.10053/0.02513 J. Integrating signed emf over that turn gives zero V·s, but integrating load power gives positive joules. All these values are calculated.
12. Peak, RMS and mean: Generated emf peaks at 2 V in that run, while its RMS value is √2≈1.414 V and its signed mean is zero. RMS means square, average, then take the square root. It connects an AC waveform to resistive heating; it is not the same as its peak. The glow uses cycle-mean load power for a calm visual cue, not a simulated filament temperature.
13. Power and efficiency ask different questions: The 2 Ω load receives more power than the 8 Ω load at the same prescribed speed, but a larger fraction also heats the winding. In this fixed-speed resistive model, RL=Rc maximizes load power, with half the modeled input becoming winding heat. This is a mathematical operating comparison, not advice to short or modify a real generator.
14. One loop is not every generator: Continuous slip rings keep winding connections intact. A brushed DC machine uses a commutator to change connections; other generators use different field, winding and rectifier arrangements. One electrical cycle per mechanical revolution describes this simple loop model, not every multi-pole alternator.
15. What Faraday actually recorded: In his first series, paragraphs 39–40, Faraday describes an indicator responding when a magnet enters a coil, returning while it is held there, and reversing on withdrawal or continued passage through. Paragraph 43 describes an outside-coil control against direct action on the indicator. These are qualitative observations, not the numerical curves in this lesson.
16. Construction has a history: The Smithsonian’s Edison type Z DC dynamo, about 1881, has wound fields and a commutator. Its Westinghouse single-phase AC generator, about 1888, has a different housing, field-coil and collector arrangement. Jaclyn Nash photographed both in 2022. Their source-owned photographs show real construction; our transparent tabletop mechanism is original teaching geometry, not a reconstruction of hidden museum parts.

What has been checked

Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.

Each source supports the associated claim. Sources do not certify this implementation or its visuals.

About the cover illustration

Actual Brytalearn browser render of original tabletop AC generator teaching geometry: crank, coil, two continuous slip rings, fixed brushes and resistive lamp. Calculated prescribed-motion model, not a scan, museum replica or measured apparatus. Separate Smithsonian museum photographs are credited inside the lesson.