In a DC motor, the split-ring commutator:

Reverses the current in the coil every half turn

Changes AC into DC from the mains

Motors, Generators and Power Transmission

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.

$τ = n I A B sin θ$

$n$ = number of turns, $I$ = current, $A$ = area of the coil, $B$ = field
$θ$ = 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.

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.

$I = \frac{V _{s u ppl y} - ε _{ba c k}}{R}$

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.

AC in the stator coils makes a magnetic field that rotates around the motor.
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.
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:

$P_{l oss} = I^{2} R$

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

A step-up transformer raises the voltage at the power station (to hundreds of kilovolts).
Power travels along the transmission lines at high voltage and low current.
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.

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 12Calculating transmission losses

A power station sends 500 kW along lines with a total resistance of 4.0 Ω.

At 10 kV: $I = \frac{500 000}{10 000} = 50$ A. Loss $= 5 0^{2} \times 4.0 = 10000$ 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 $P = \frac{V ^{2}}{R}$ for the line must be the voltage drop along the line, not the transmission voltage. Using $I^{2} R$ 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 $I R$ 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 $τ = n I A B$ : 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 $m g d$ . The coil is held still when $n I A B = m g d$ .

Generator output. A coil spinning at angular velocity $ω$ has peak emf $ε = N B A ω$ , with $ω = 2 π f$ (3000 rpm is 50 rev/s, so $ω = 314$ rad/s). Halving the speed halves both the peak emf and the frequency.

Chains of transformers. Use $\frac{V _{p}}{V _{s}} = \frac{N _{p}}{N _{s}}$ 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 $I = \frac{V}{R _{coil} + R _{start}}$ . 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: $τ = n I A B sin θ$ , 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 $I^{2} R$ losses. Transformers step it up and down.

Quiz

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In a DC motor, the split-ring commutator:
1. A Makes the magnetic field
2. B Reverses the current in the coil every half turn
3. C Changes AC into DC from the mains
4. D Stops the motor overheating
Show answer
B: Reverses the current in the coil every half turn
Reversing the current keeps the torque turning the coil the same way.
A motor coil has the most torque when its plane is:
1. A Face-on to the field
2. B Parallel to the field
3. C At 45° to the field
4. D Moving fastest
Show 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.
Which change would NOT increase the torque of a DC motor?
1. A More turns on the coil
2. B More current
3. C A stronger magnet
4. D Thicker brushes
Show answer
D: Thicker brushes
Torque = nIAB sin θ. Brushes only carry the current in.

Motors, Generators and Power Transmission

Torque on a coil

The DC motor

Back emf

Generators

AC induction motors

Getting electricity to your home

Quick summary

Quiz

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