# Motors, Generators and Power Transmission

> How DC motors, generators and AC induction motors work, why motors make back emf, and how electricity reaches your home.

From HSC Physics on WhizzNotes, free study notes for NSW students: https://whizznotes.com/physics/motors-and-generators/. Updated 2 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: Two machines, one design
Jordan takes apart a small toy motor and connects its two wires to a light bulb. Then he spins the shaft quickly between his fingers. The bulb flickers on.

"It's a motor," says his sister. "Motors use electricity. They don't make it."

"Turns out it's both," says Jordan. A motor puts current through a coil in a magnetic field, and the coil spins. A generator spins a coil in a magnetic field, and a current comes out. It is the same machine running in two directions. Electric cars use this every day: the motor drives the wheels, and when braking it becomes a generator that recharges the battery.

**In short:** A motor turns electrical energy into rotation, because a current-carrying coil in a magnetic field feels a turning force (torque). A generator does the reverse, turning rotation into electricity by induction. Power lines carry electricity at high voltage and low current to cut energy losses.

## Torque on a coil

A flat coil carrying a current sits in a magnetic field. The two sides that cross the field feel forces in **opposite directions** (motor effect). These forces make a **torque** that turns the coil.

$$\tau = nIAB\sin\theta$$

- $n$ = number of turns, $I$ = current, $A$ = area of the coil, $B$ = field
- $\theta$ = angle between the field and the **normal** to the coil

The torque is **largest** when the plane of the coil is **parallel** to the field. It is **zero** when the coil is face-on to the field, because then the forces pull straight outwards and have no turning effect.

### Worked example: A motor coil
A 50-turn coil measures 0.040 m by 0.050 m and carries 2.0 A in a 0.30 T field, with its plane parallel to the field.

$\tau = 50 \times 2.0 \times (0.040 \times 0.050) \times 0.30 \times 1 = 0.060$ N m.

## The DC motor

A simple DC motor has these parts:

| Part | Job |
|---|---|
| **Stator** (magnets) | provides the magnetic field; does not move |
| **Armature** (rotor coil) | carries current and turns |
| **Split-ring commutator** | reverses the current in the coil every half turn |
| **Brushes** | carbon blocks that press on the commutator to carry current in |

Why the commutator? Without it, the coil would turn half a turn, then the forces would push it back, and it would rock to a stop. The commutator flips the current each time the coil passes face-on, so the torque always turns it the **same way**.

Making a motor more powerful: more turns, more current, a stronger field, a bigger coil area. Many motors also curve the magnets into a **radial field**, so the coil's sides always cut the field at right angles. Then the torque stays at its maximum as the coil turns.

## Back emf

A spinning motor coil is also a coil moving in a magnetic field, so it acts as a **generator** too. It makes an emf that **opposes** the supply voltage (Lenz's law). This is called **back emf**.

- When the motor **starts**, it is not spinning, so there is no back emf. The current is very large.
- As it **speeds up**, the back emf grows and the current falls.
- When a **load** is added, the motor slows, the back emf falls and the current rises.

$$I = \frac{V_{supply} - \varepsilon_{back}}{R}$$

Large motors use a **starting resistor** to limit the huge current at start-up, so the coil does not overheat.

## Generators

A generator spins a coil in a magnetic field. The changing flux induces an emf (Faraday's law).

- **AC generator**: uses **slip rings**, which keep each end of the coil connected to the same output wire. The output is a sine wave that reverses every half turn.
- **DC generator**: uses a **split-ring commutator**, which swaps the connections every half turn. The output always has the same sign, rising and falling like bumps.

Spinning faster gives a **bigger** emf and a **higher frequency**, because the flux changes faster.

## AC induction motors

An **AC induction motor** has no brushes or commutator.

1. AC in the **stator** coils makes a magnetic field that **rotates** around the motor.
2. The **rotor** is a "squirrel cage" of metal bars joined by end rings. The rotating field sweeps past the bars and induces currents in them.
3. These induced currents feel a force in the field (motor effect), so the rotor is dragged round after the field.

The rotor always turns a bit **slower** than the field. If it caught up, there would be no relative motion, no change in flux and no induced current. Induction motors are tough and cheap, which is why they run washing machines, fans and pumps.

## Getting electricity to your home

Power stations are far from cities. The wires between them have resistance, and they waste power as heat:

$$P_{loss} = I^2 R$$

Since power is $P = VI$, sending the same power at a **high voltage** needs only a **small current**. Halving the current cuts the loss to one quarter. So:

1. A **step-up** transformer raises the voltage at the power station (to hundreds of kilovolts).
2. Power travels along the transmission lines at high voltage and low current.
3. **Step-down** transformers at substations lower it in stages to 230 to 240 V for homes.

This is why the grid uses **AC**: transformers only work with a changing current.

**Mind map**

```text
Motors and Generators
  DC motor
    τ = nIAB sin θ
    Split-ring commutator
    Brushes, stator, armature
    Radial field
  Back emf
    Opposes supply
    Big current at start
    Starting resistor
  Generators
    AC: slip rings
    DC: split ring
    Faster: more emf
  Induction motor
    Rotating field
    Squirrel cage rotor
    Rotor lags the field
  Transmission
    P loss = I²R
    High voltage, low current
    Step up, then step down
```

### Year 11: Energy in motors and generators
A motor changes **electrical** energy into **kinetic** energy. A generator changes **kinetic** energy into **electrical** energy. Neither is perfect: some energy always becomes heat in the coil's resistance and through friction.

**Regenerative braking**: when an electric car brakes, its motor is switched to work as a generator. The wheels turn the coil, the induced current charges the battery, and the opposing force (Lenz's law) slows the car. Kinetic energy becomes stored energy instead of heat in brake pads.

### Year 12: Calculating transmission losses
A power station sends 500 kW along lines with a total resistance of 4.0 Ω.

- At 10 kV: $I = \dfrac{500\,000}{10\,000} = 50$ A. Loss $= 50^2 \times 4.0 = 10\,000$ W (2% of the power).
- At 100 kV: $I = 5.0$ A. Loss $= 5.0^2 \times 4.0 = 100$ W (0.02%).

Raising the voltage 10 times cut the loss 100 times.

**Careful:** the voltage in $P = \dfrac{V^2}{R}$ for the line must be the **voltage drop along the line**, not the transmission voltage. Using $I^2R$ with the line current avoids this trap.

**Motor graphs.** On a graph of current against time for a DC motor, the current starts at its maximum (no back emf) and falls as the motor speeds up, levelling off at the operating speed. Torque in a motor follows the current.

**Voltage at the far end.** The line drops $IR$ volts. Sending 2.0 MW at 22 kV gives $I = 91$ A; with 8.0 Ω the drop is 727 V, so the far end receives about 21.3 kV.

**Comparing motors.** Use ratios of $\tau = nIAB$: doubling $n$ and $A$, halving $I$ and taking $\frac{3}{4}$ of $B$ multiplies the torque by $2 \times 2 \times \frac{1}{2} \times \frac{3}{4} = 1.5$.

**Holding a motor still.** A hanging mass $m$ at distance $d$ from the axle gives a torque $mgd$. The coil is held still when $nIAB = mgd$.

**Generator output.** A coil spinning at angular velocity $\omega$ has peak emf $\varepsilon = NBA\omega$, with $\omega = 2\pi f$ (3000 rpm is 50 rev/s, so $\omega = 314$ rad/s). Halving the speed halves both the peak emf and the frequency.

**Chains of transformers.** Use $\dfrac{V_p}{V_s} = \dfrac{N_p}{N_s}$ for each transformer separately. Stepping 33 kV down to 240 V with 3300 primary turns needs $3300 \times \frac{240}{33\,000} = 24$ secondary turns.

**Odd set-ups.** A DC motor (permanent magnets, split ring) on AC just buzzes: the current reverses 50 times a second, so the torque keeps reversing before the coil can turn. In a home-made coil motor, sanding the insulation off only half of each wire end lets current flow for only half of each turn, which does the commutator's job.

**Starting resistors.** At start-up there is no back emf, so $I = \dfrac{V}{R_{\text{coil}} + R_{\text{start}}}$. To keep 24 V to 5.0 A with a 0.80 Ω coil, the total resistance must be 4.8 Ω, so add 4.0 Ω.

**Induction motor speed and loads.** Raising the AC supply frequency makes the stator field rotate faster, so the rotor turns faster. Eddy current braking on a spinning disc is an extra load: the motor slows, the back emf falls and the current rises.

## Quick summary

- Torque on a coil: $\tau = nIAB\sin\theta$, largest when the coil's plane is parallel to the field.
- A DC motor uses a split-ring commutator to reverse the current every half turn.
- Spinning motors make a back emf that opposes the supply, so the current is largest at start-up.
- AC generators use slip rings. DC generators use a split-ring commutator.
- Induction motors use a rotating field to induce currents in the rotor.
- Power is sent at high voltage and low current to reduce $I^2R$ losses. Transformers step it up and down.

## Quiz

Try these questions from the chapter quiz.

1. In a DC motor, the split-ring commutator:
   - A. Makes the magnetic field
   - B. Reverses the current in the coil every half turn
   - C. Changes AC into DC from the mains
   - D. Stops the motor overheating
   - Answer: B. Reverses the current in the coil every half turn. Reversing the current keeps the torque turning the coil the same way.

2. A motor coil has the most torque when its plane is:
   - A. Face-on to the field
   - B. Parallel to the field
   - C. At 45° to the field
   - D. Moving fastest
   - Answer: B. Parallel to the field. When the coil's plane is parallel to the field, the forces are furthest from the axle and at right angles to it.

3. Which change would NOT increase the torque of a DC motor?
   - A. More turns on the coil
   - B. More current
   - C. A stronger magnet
   - D. Thicker brushes
   - Answer: D. Thicker brushes. Torque = nIAB sin θ. Brushes only carry the current in.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/physics/motors-and-generators/#quiz