Year 12 Physics Module 6 ⏱ ~40 min 5 MC · 2 Short Answer Lesson 11 of 21 IQ4: Motor technologies

DC and AC Motors Overview

A brushed DC motor switches current mechanically. An induction motor transfers energy across an air gap using a rotating magnetic field. Comparing those pathways explains why the machines differ in starting, control and maintenance.

Today's hook: A battery motor can reverse torque every half-turn using copper contacts. An induction motor has no powered rotor connection at all. How can both convert electrical input into continuous rotation?
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Orient and compare

Retrieve the motor effect, then predict why two motor designs need different ways to sustain torque.

Warm up first

Three quick questions from earlier lessons. Pulling old material back to mind before you learn something new makes the new material stick better, so this is not busywork.

Worksheets

Practise this lesson

Use the available foundations worksheet for guided practice on this lesson.

Build Foundations & guided practice
Before you read, predict

A simple brushed DC motor uses a split-ring commutator to reverse current every half-turn. A squirrel-cage induction motor has no powered rotor contacts or commutator.

  1. Why does the brushed DC motor need a split-ring current reversal, while the squirrel-cage induction motor does not?
  2. Which motor type would be simpler to maintain? Why?
  3. How could an induction motor produce rotor current without any powered contact to the rotor?

Warm-up, a DC motor converts electrical energy into…

Learning Intentions
goals

Know, Motor Structures

  • DC motor: split-ring commutator, brushes, radial magnetic field
  • AC induction motor: stator with rotating magnetic field, no commutator
  • Back emf opposes the applied voltage in a running motor

Understand, How They Work

  • The commutator reverses current so torque is always in the same direction
  • In an induction motor, the rotating stator field induces current in the rotor
  • Back emf increases with motor speed, limiting the current drawn

Can Do, Analyse and Compare

  • Compare DC and AC motor designs and their advantages
  • Explain back emf and its effect on motor current and stall heating
  • Select appropriate motor types for given applications
Scan these before reading
vocab
Back emf (ε)The voltage induced in a motor's coil as it rotates, opposing the applied voltage. Increases with speed.
Split-ring commutatorA ring split into two halves that reverses current direction every half-turn in a DC motor.
StatorThe stationary part of a motor (usually the magnets or electromagnets).
RotorThe rotating part of a motor (usually the coil or squirrel cage).
Induction motorAn AC motor where the rotating magnetic field of the stator induces current in the rotor, creating torque without direct electrical connection.
SlipThe difference between rotating stator-field speed and rotor speed. Relative motion is required to induce rotor current and torque.
Misconceptions to fix
✗ Wrong: Back emf is a separate component added inside the motor.
✓ Right: Back emf is the emf induced in the rotating coil by its own motion through the magnetic field, Faraday's Law in action inside the motor.
✗ Wrong: An AC induction motor works by reversing the current in the rotor every half cycle.
✓ Right: The rotor has no direct electrical connection to the supply. Torque is produced by electromagnetic induction, the rotating stator field induces currents in the rotor, which then interact with that field.
✗ Wrong: A DC motor draws the same current whether it is running at full speed or stalled.
✓ Right: At stall, back emf is zero, so winding resistance limits current to the finite maximum $V/R$. At high speed, back emf is large and current falls to the value required by load and losses.
Cross-lesson links: L09 showed how a coil in a field produces torque. L10 applies this to practical motors, DC motors use a commutator to maintain torque direction; AC induction motors use a rotating field instead. Understanding both types is required for the HSC 'describe the role of the commutator' question type.
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DC structure

Keep DC torque turning one way

Trace current, forces and contact changes through each half-turn of a simple brushed DC motor.

Core Content

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DC Motor: Design and Operation
+5 XP

Continuous rotation through clever switching

Connect a DC motor to a battery and watch the shaft spin continuously in one direction. Without any electronic control, it just spins, and keeps spinning. But there is a hidden problem: as the coil turns through 180°, the forces on its sides would naturally reverse, trying to spin it backwards. The commutator, two copper half-rings that swap the current connections every half-turn, is what prevents this reversal and keeps the torque acting in the same rotational direction throughout each revolution.

The split-ring commutator solves this. It is a metal ring split into two halves, each connected to one end of the coil. Brushes press against the commutator to supply current. Every half-turn, the brushes switch from one half-ring to the other, reversing the current in the coil. This keeps the torque pushing in the same rotational direction.

Field and coil

The stator supplies the magnetic field. Current in opposite coil sides experiences opposite forces, forming a torque pair.

Contacts and switching

Brushes supply current to the rotating split ring. Each half-turn swaps the coil connections so torque keeps the same rotational sense.

Radial-field model

Shaped pole pieces can keep the field approximately parallel to the coil plane, so it remains nearly perpendicular to the coil's area normal. In the ideal model this keeps the torque factor near its maximum during rotation.

Stop & Check

A DC motor stalls (stops spinning) when too much load is applied. Explain why the current drawn by the motor increases dramatically when it stalls. (Hint: what happens to back emf at zero speed?)

DC motor components: coil (rotor), field source (stator), split-ring commutator (reverses current every half-turn), brushes (sliding contact), radial field (keeps the ideal torque factor near its maximum). The commutator keeps torque in one rotational direction; multiple coils smooth the output further.

Pause, copy the highlighted DC motor components and their functions into your book before moving on.

The purpose of the split-ring commutator in a DC motor is to:

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Energy overview

Connect speed, back emf and current

Use the DC circuit relation at overview depth and identify why stall current is finite but large.

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Back emf in DC Motors
+5 XP

The motor that generates while it spins

We just saw how a DC motor's commutator and radial field keep the coil spinning continuously. That raises a question: as the coil spins through the field, does it also act like a generator? This card answers it → yes, the rotating coil induces a back emf that opposes the supply, limiting current to $(V - \varepsilon_\text{back})/R$.

As a DC motor's coil rotates through a magnetic field, it experiences changing magnetic flux. By Faraday's Law, this induces an emf in the coil. By Lenz's Law, this induced emf opposes the change that created it, so it opposes the applied voltage. This is back emf.

Back emf and Motor Current

$I = \dfrac{V - \varepsilon_{\text{back}}}{R}$

  • I = current through motor (A)
  • V = applied voltage (V)
  • εback = back emf (V)
  • R = coil resistance (Ω)

When the motor starts from rest, back emf is zero and the current is maximum ($I = V/R$). As speed increases, back emf grows, reducing the net voltage and thus the current. At a light-load steady speed, back emf may be close to $V$, and the current drops to the value required by the load and losses.

HSC Tip

Back emf is not a separate component; it is induced by rotation. In general $\varepsilon_{\text{back}}=k_e\omega$, where $k_e$ depends on construction and flux. The special result $NBA\omega$ is an ideal simple-coil maximum, not a universal motor equation. At stall, $\omega=0$, so resistance limits current to $V/R$.

Worked Example, Back emf and Motor Current

A DC motor has coil resistance 2.0 Ω and is connected to a 12 V supply. When running at full speed, the back emf is 10 V.

  1. Part (a), Running current. $I = \dfrac{V - \varepsilon_{\text{back}}}{R} = \dfrac{12 - 10}{2.0} = 1.0$ A
  2. Part (b), Stall current. When stalled, $\omega = 0$ so $\varepsilon_{\text{back}} = 0$. $I_{\text{stall}} = \dfrac{12}{2.0} = 6.0$ A
  3. Part (c), Explanation. Back emf is proportional to motor speed. At full speed, the 10 V back emf opposes most of the 12 V supply, leaving only 2 V to drive current. When stalled, no back emf exists so the full 12 V drives current through the coil, explaining why stall conditions can overheat motors.

Back emf (Lenz's Law): $I = (V - \varepsilon_\text{back})/R$. At start: $\varepsilon_\text{back} = 0$ → $I_\text{max} = V/R$. At light load and high speed: larger back emf → smaller current. At stall: $\varepsilon_\text{back} = 0$ again → current rises to $V/R$ and prolonged stall can overheat the windings.

Add the highlighted back emf equation and three operating states to your notes before the check below.

A DC motor connected to 24 V has coil resistance 4.0 Ω. At full speed, back emf is 20 V. The running current is:

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AC structure

Transfer torque across an air gap

Follow the chain from a rotating stator field to induced rotor current, magnetic force and slip.

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AC Induction Motors
+5 XP

No brushes, no commutator, no direct rotor connection

We just saw how back emf limits current in a spinning DC motor. That raises a question: is there a motor design that avoids brushes and commutators entirely, eliminating the wear and sparking problems? This card answers it → yes, the AC induction motor uses electromagnetic induction to transfer torque to the rotor with no direct electrical connection.

An AC induction motor has two main parts: a stator (stationary electromagnets) and a rotor (usually a squirrel cage, metal bars shorted at both ends). There are no brushes and no commutator.

Appropriately spaced stator windings supplied by polyphase AC, or by phase-shifted currents in some single-phase designs, create a rotating magnetic field. Alternation in one coil alone gives a pulsating field, not automatically a self-starting rotating field. The moving stator field cuts the squirrel-cage conductors and induces rotor currents. Those currents experience magnetic forces in the stator field, producing torque.

Key advantage

No physical electrical connection to the rotor means no brushes to wear out, no sparks, and very low maintenance. This is why induction motors are used in washing machines, fans, pumps, and industrial machinery.

Why slip is required: In ordinary motoring operation under load, the rotor turns below the rotating-field speed. If rotor and field had the same angular speed, their relative motion would vanish, so induced rotor emf, rotor current and electromagnetic torque would fall to zero. A loaded rotor therefore slows and slip reappears; detailed synchronous-speed and slip calculations belong to L16.

HSC Tip

An induction motor needs no split-ring commutator because the supplied stator windings create the moving field and rotor current is induced without powered sliding contacts. The reason is the rotating-field arrangement, not merely that one current alternates.

AC induction motor: phase-displaced stator currents → rotating magnetic field → induced squirrel-cage rotor currents → magnetic force and torque. No powered rotor contact or split-ring commutator is required. Non-zero slip maintains relative motion and induction while the motor supplies load torque.

Pause, write the highlighted induction motor structure and operating principle into your book before moving on.

A squirrel-cage induction motor needs no split-ring commutator because:

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Compare

Choose a motor from its operating conditions

Compare energy transfer, contacts, control and maintenance without assuming one design is always best.

Brushed DC motor

Powered rotor coil, brushes and split ring. Simple direct-voltage control and strong starting current, with contact wear and sparking.

Induction motor

Powered stator and unpowered squirrel-cage rotor. Robust and low-maintenance; electronic variable-frequency control is used when a wide speed range is required.

Interactive Tool, Motors & Generators Open fullscreen ↗

Use the interactive only for the motor overview. Generator modes are L11/L16 previews and are not required to answer this lesson's questions.

When a DC motor slows down under load, the current increases because:

Comparative-overview boundary

L10 compares structures and energy-conversion principles. L17 owns the detailed DC equivalent circuit, torque-speed/current-speed graphs and power ledger. L16 owns three-phase rotating fields, synchronous-speed and slip calculations, and power-station generators. Do not transfer the DC commutator/back-emf model directly to an induction motor.

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Apply

Explain and calculate

Apply the structural comparison and the finite-current model before independent Practice.

Activity 1, Compare Motor Designs
ApplyBand 4

Use your notes and the interactive to compare DC and AC motors

  1. Why does a DC motor draw more current when it starts than when it runs at full speed?
  2. List one advantage and one disadvantage of an AC induction motor compared to a DC motor.
  3. A variable-speed industrial drive must be low-maintenance and has a suitable electronic controller. Which design is a defensible choice? State the evidence and one limitation of your decision.
  4. Explain in your own words why rotor slip is essential for an induction motor to work.
Activity 2, Back emf Calculations
ApplyBand 4

Use the overview relation without extending into the L17 power ledger

  1. A motor with $R = 3.0\,\Omega$ is connected to $15$ V. At full speed it draws $1.0$ A. Calculate the back emf.
  2. The same motor stalls. Calculate the stall current and explain why this is dangerous.
  3. The motor is protected by a 4.0 A fuse. Decide whether the fuse should interrupt the stalled circuit, using your calculated stall current.
Synthesis, connect the ideas
  • DC motors use a split-ring commutator to reverse current, keeping torque in one direction.
  • Back emf is induced in the rotating coil and opposes the applied voltage, limiting current.
  • Induction motors need no powered rotor contacts: a deliberately rotating stator field induces rotor current.
  • Motor selection depends on supply, controller, torque-speed needs, maintenance and environment; neither design is universally superior.
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Independent practice

Show what you can do without prompts

Complete a shuffled bank set, then explain one DC operating change and compare the two motor pathways.

Quick recall, DC and AC Motors
+5 XP

A fresh five-question set drawn from this lesson's bank, feedback shown immediately. +5 XP per correct · +25 XP all correct

Pick your answer, then rate your confidence, that tells the system what to drill next.

Short Answer, 7 marks
+5 XP

ApplyBand 4(3 marks) 1. A DC motor with coil resistance 3.0 Ω is connected to a 15 V supply. (a) Calculate the stall current. (b) When running at full speed, the motor draws 1.0 A. Calculate the back emf. (c) Explain what would happen to the current if the motor were suddenly loaded so it slowed down.

1 mark: correct stall current · 1 mark: correct back emf with working · 1 mark: explanation links speed to back emf to current

AnalyseBand 5(4 marks) 2. Compare a simple brushed DC motor and a squirrel-cage induction motor. In your answer explain how continuous torque is produced, why their rotor connections differ, and one operating trade-off that depends on the application.

1 mark: DC torque pair and half-turn current reversal · 1 mark: rotating stator field induces rotor currents and forces · 1 mark: contrasts powered brushes/commutator with unpowered cage · 1 mark: justified application-dependent trade-off

Show all answers

Multiple choice

MC answers and full explanations are shown inline as you complete each question. Use the retry button to attempt a fresh set drawn from the lesson bank.

Short Answer, Model Answers

Q1 (3 marks): (a) At stall, $\varepsilon_{\text{back}} = 0$, so $I = V/R = 15/3.0 = 5.0$ A (1 mark). (b) $\varepsilon_{\text{back}} = V - IR = 15 - (1.0)(3.0) = 12$ V (1 mark). (c) Slowing down reduces the motor's angular velocity, which reduces the back emf (back emf ∝ speed). The smaller back emf means the net voltage driving current through the coil increases, so the current increases (1 mark).

Q2 (4 marks): In a brushed DC motor, forces on opposite current-carrying coil sides form a torque pair. The split-ring commutator reverses coil current every half-turn so the torque retains the same rotational sense (1 mark). In a squirrel-cage induction motor, phase-displaced stator currents create a rotating magnetic field. Relative motion induces rotor currents, whose magnetic forces produce torque (1 mark). The DC rotor is powered through brushes and a commutator, whereas the cage rotor is short-circuited and unpowered by direct contacts (1 mark). A defensible trade-off is that the induction motor removes brush wear and sparking, while wide-range speed control generally requires a suitable variable-frequency drive; the best choice therefore depends on the supply, controller, load and maintenance conditions (1 mark).

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Final step

Retrieve, reflect and finish

Check what stuck, revisit the opening comparison and state the causal chain for each motor.

Check what actually stuck
Take the full module quiz
quiz

A full module quiz covering every lesson in this module, not just this one. Set aside a decent block of time and treat it like a real assessment.

Start the module quiz →
Revisit Your Thinking

At the start you compared mechanical current switching with contact-free induction. A brushed DC motor maintains torque direction by reversing rotor-coil current every half-turn. An induction motor instead uses phase-displaced stator currents to create a rotating field, which induces current and force in its unpowered cage rotor.

When the DC motor slows, $\varepsilon_{\text{back}}=k_e\omega$ decreases, so $I=(V-\varepsilon_{\text{back}})/R$ increases. At stall, resistance keeps the current finite at $V/R$, although that value can be large enough to overheat the windings. In an induction motor, increasing load normally increases slip, which changes induced rotor current and torque; the detailed torque-slip relationship is developed in L16.

Now extend: A DC motor is connected to a 12 V battery. When running freely, it draws 1.5 A. When loaded so it slows down, the current increases to 3.0 A. Explain why slowing down causes the current to increase, and use the formula $I = (V - \varepsilon_{\text{back}})/R$ to find the back emf in each case (coil resistance = 2.0 Ω).

← Previous: Torque on a Current-Carrying Coil Next: DC Motors in Depth →

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