How a Machine Converts Energy
Start here. Run one loop of wire as a generator, then reverse the arrow and run the identical hardware as a motor.
Skip to the animationEvery electrical machine is a conductor and a magnetic field in relative motion: Faraday's law says the changing flux linkage produces a voltage, Lenz's law says the resulting current always opposes whatever caused it, and that opposition is precisely how energy crosses between the electrical and mechanical domains.
Generator action
Move a loop of wire through a magnetic field and the flux linking it changes. Faraday's law says an EMF appears: e = −N·dΦ/dt. It is the *rate of change* that matters — a loop sitting still in the strongest available magnet generates nothing at all.
Leave the loop open-circuit and that is the end of it: a voltage exists, no current flows, and the loop is as easy to move as it ever was. Close the circuit and everything changes.
Lenz's law is the whole mechanism
- 1Current flows, because there is now a closed path.
- 2That current creates a magnetic field of its own, as any current does.
- 3Lenz's law: that field opposes the change that produced it.
- 4So a force appears resisting the motion, and you must do more work to keep the loop moving.
- 5The extra mechanical work you do is exactly the electrical energy delivered.
This is why an unloaded generator spins freely and a loaded one is heavy. That difference in effort is the power being generated — it is not a side effect of generation, it *is* generation.
The minus sign is not a formality. If the induced current helped the motion, a nudge would produce current, which would produce more motion, which would produce more current. Lenz's law is what makes the machine a converter rather than a perpetual motion machine.
Motor action is the same machine, backwards
A current-carrying conductor in a magnetic field experiences a force, F = B·I·L. Force current into the same loop and it turns. Nothing about the machine has changed — not the windings, not the magnets, not the wiring. Only the direction of energy flow.
This is not a curiosity. A hybrid car uses one machine to drive the wheels and then, unchanged, to recover energy under braking. A generator driven backwards runs as a motor, and a motor spun by its load generates.
Back-EMF, and why a stalled motor burns out
A running motor's conductors are moving through a field, so they are generating — whether anyone wants them to or not. By Lenz's law that EMF opposes the applied voltage, and it is called the back-EMF.
The armature current is therefore I_a = (V − E_b)/R_a. Since E_b ∝ ωΦ, the speed determines the current rather than the other way round. A lightly loaded motor speeds up until the back-EMF nearly cancels the supply, and it draws almost nothing.
At standstill E_b = 0, so the only thing limiting the current is the small armature resistance — often a few tenths of an ohm. This is why starting current can be ten times the running current, and why any large motor needs a starter.
The four device families, as arrangements of one idea
| Machine | How the relative motion is arranged | The consequence |
|---|---|---|
| Transformer | No motion — the field is changed electrically by AC | Works only on AC; no DC transformer exists |
| DC machine | A commutator reverses the connection twice per revolution | Unidirectional torque, at the cost of brushes that wear |
| Induction machine | Rotor current is *induced*, not supplied | The rotor must lag the field, which is slip — at exact synchronism it would produce no torque at all |
| Synchronous machine | Both fields supplied; the rotor locks to the stator field | Constant speed set by frequency; will not start on its own |
The induction motor row is the one worth dwelling on. If the rotor ever reached synchronous speed there would be no relative motion, no changing flux, no induced current and therefore no torque. Slip is not an inefficiency to be eliminated — it is the condition under which the machine works.
Where the energy actually goes
- Copper loss —
I²Rin the windings. Rises with load, and is what current rating is really about. - Iron loss — hysteresis and eddy currents in the core. Roughly constant with load, which is why laminations and silicon steel exist.
- Friction and windage — bearings and air resistance, essentially constant.
- Stray load loss — everything the model does not account for, conventionally about 1%.
Maximum efficiency occurs where the variable loss equals the constant loss. That is a general result about machines, and it is why a motor run far below its rating is inefficient even though it is drawing little current.
The numbers you will be asked for
- Faraday's law
e = −N · dΦ/dt
The minus sign is Lenz's law; it is the physics, not the bookkeeping.
- Force on a conductor
F = B·I·L
Motor action. With the flux and length fixed, torque is proportional to current.
- Motional EMF
e = B·L·v
Generator action for a straight conductor moving at v.
- Armature current
I_a = (V − E_b) / R_a
E_b ∝ ωΦ, so speed sets the current. At standstill only R_a limits it.
- Mechanical power
P = T·ω = E_b·I_a
The converted power, before friction and windage are subtracted.
Advantages and disadvantages
Advantages
- One principle covers transformers, DC, induction and synchronous machines.
- The conversion is inherently reversible — the same machine motors and generates.
- Efficiency is high, routinely above 95% for large machines, because no combustion is involved.
- Torque follows current directly, which makes the machine straightforward to control.
Disadvantages
- Requires a magnetic circuit, so machines are heavy — iron and copper, not electronics.
- Iron loss is present whenever the machine is energised, whether or not it is doing work.
- Starting current is limited only by winding resistance, so starters are mandatory above small sizes.
- Commutators and brushes wear and spark, which is much of the reason induction motors displaced DC ones.
Watch it work
Check yourself
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