DC and AC Motors
On 16 May 1888, Nikola Tesla demonstrated his two-phase AC induction motor to the American Institute of Electrical Engineers in New York — no brushes, no commutator, just a rotating magnetic field inducing currents in a squirrel-cage rotor. He sold the patents to George Westinghouse for $1 million plus $2.50 per horsepower royalty. Today's Tesla Model 3 rear motor (211 kW, 430 N·m) is a direct descendant of that 1888 design.
Practise this lesson
Four printable worksheets that build from the foundations up to exam-style questions — start at whatever level suits you.
A DC motor uses a split-ring commutator to reverse current every half-turn. An AC induction motor has no commutator at all.
- Why does a DC motor need to reverse its current, but an AC motor does not?
- Which motor type would be simpler to maintain? Why?
- Your house runs on AC power. Could you plug a DC motor straight into a wall socket?
Warm-up — a DC motor converts electrical energy into…
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 power
- Select appropriate motor types for given applications
Core Content
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.
| Feature | Function |
|---|---|
| Radial magnetic field | Keeps torque nearly constant throughout rotation |
| Split-ring commutator | Reverses current every half-turn for continuous rotation |
| Brushes | Maintain electrical contact with rotating commutator |
| Multiple coils | Smoother torque — one coil is always at maximum torque |
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), permanent magnets (stator), split-ring commutator (reverses current every half-turn), brushes (sliding contact), radial field (constant torque). Split-ring 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:
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.
$I = \dfrac{V - \varepsilon_{\text{back}}}{R}$
- 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 maximum speed, back emf is nearly equal to $V$, and the current drops to just enough to overcome friction and load.
Back emf is not a separate component — it is the emf induced in the coil by its own rotation. It is proportional to motor speed: $\varepsilon_{\text{back}} = NBA\omega$ for a simple coil. When the motor stalls ($\omega = 0$), back emf = 0 and current surges to $V/R$.
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.
- Part (a) — Running current. $I = \dfrac{V - \varepsilon_{\text{back}}}{R} = \dfrac{12 - 10}{2.0} = 1.0$ A
- Part (b) — Stall current. When stalled, $\omega = 0$ so $\varepsilon_{\text{back}} = 0$. $I_{\text{stall}} = \dfrac{12}{2.0} = 6.0$ A
- 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 full speed: $\varepsilon_\text{back} \approx V$ → $I_\text{min}$. At stall: $\varepsilon_\text{back} = 0$ again → current surges to $V/R$ and motor overheats.
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:
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.
The stator is connected to AC power, which creates a rotating magnetic field. This changing field passes through the rotor, inducing currents in the squirrel cage bars (by electromagnetic induction). These induced currents create their own magnetic field, which interacts with the stator field to produce torque.
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.
Key limitation: The rotor always turns slightly slower than the rotating magnetic field — this "slip" is necessary for induction to occur. The rotor can never reach the synchronous speed of the field.
An AC induction motor has no commutator because the AC current already alternates direction. The stator coils themselves create a rotating field — no mechanical switching is needed.
AC induction motor: stator (AC electromagnets) + squirrel-cage rotor. No brushes, no commutator, no direct rotor connection. AC stator → rotating field → induced rotor currents → torque. Rotor always lags field ("slip"): a changing field is essential for induction.
Pause — write the highlighted induction motor structure and operating principle into your book before moving on.
An AC induction motor has no commutator because:
When a DC motor slows down under load, the current increases because:
Use your notes and the interactive to compare DC and AC motors
- Why does a DC motor draw more current when it starts than when it runs at full speed?
- List one advantage and one disadvantage of an AC induction motor compared to a DC motor.
- A train needs high starting torque and variable speed. Would you choose a DC or AC motor? Justify.
- Explain in your own words why rotor slip is essential for an induction motor to work.
Practise using the back emf formula in different scenarios
- A motor with $R = 3.0\,\Omega$ is connected to $15$ V. At full speed it draws $1.0$ A. Calculate the back emf.
- The same motor stalls. Calculate the stall current and explain why this is dangerous.
- A motor runs freely drawing $2.0$ A from a $12$ V supply. Its coil resistance is $1.5\,\Omega$. Find the back emf and the power dissipated as heat in the coil.
- 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.
- AC induction motors have no commutator — the rotating stator field induces current in the rotor.
- DC motors offer high starting torque and easy speed control; AC motors are simpler and more durable.
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.
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 the design and operation of a DC motor and an AC induction motor. In your answer refer to: the role of the commutator (or lack of one), how torque is produced in each motor, and the advantages and disadvantages of each type.
1 mark: DC commutator reverses current every half-turn · 1 mark: AC rotating stator field induces rotor currents (no commutator) · 1 mark: valid advantage of each type · 1 mark: valid disadvantage of each type
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 DC motor, the split-ring commutator reverses the current direction in the coil every half-turn, ensuring the magnetic force always acts in the same rotational direction and producing continuous rotation (1 mark). In an AC induction motor, there is no commutator — the three-phase AC supply to the stator creates a rotating magnetic field, which induces currents in the squirrel-cage rotor; the interaction between these induced currents and the stator field produces torque (1 mark). DC advantage: high starting torque, easy variable speed control; DC disadvantage: brushes and commutator wear, requiring maintenance (1 mark). AC advantage: no brushes, simple robust construction, low maintenance; AC disadvantage: speed less easily varied, rotor always runs slower than the field (slip), cannot start under heavy load as easily (1 mark).
Five timed questions on DC and AC motors. Beat the boss to bank a tier — gold (perfect + fast), silver (80%+), or bronze (cleared).
⚔ Enter the arenaAt the start you were asked about Tesla's 1888 AC induction motor (New York demonstration) versus a DC drill motor — why does the DC motor slow and heat up when pushed into wood, while the AC induction motor behaves differently?
The answer: when the DC motor slows, back emf drops, so more current flows ($I = (V - \varepsilon_{back})/R$), and $I^2R$ heat losses increase rapidly. Tesla's AC induction motor has no brushes — when load increases the rotor slips more relative to the rotating field, inducing more current and more torque automatically, recovering speed more gracefully.
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).