Electric Motor Examples: 46 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Electric Motor.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

A device that converts electrical energy into mechanical energy (rotational motion) by exploiting the force exerted on a current-carrying conductor placed in a magnetic field.

Run current through a loop between magnets and it spins — the magnetic force on each side of the loop pushes in opposite directions, creating rotation.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Electric Motor starts by naming the source, the object affected, and how the field or potential changes through space.

Common stuck point: Students often know a formula related to electric motor but skip the recognition step: Am I using a field or potential to explain how one object influences another across space? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I using a field or potential to explain how one object influences another across space?

Worked Examples

Example 1

easy

A DC motor draws

4 \text{ A}

from a

12 \text{ V}

supply. If the motor is

80\%

efficient, what is its useful mechanical power output?

Answer

P_{out} = 38.4 W

First step

Electrical power input:

P_{\text{in}} = VI = 12 \times 4 = 48 \text{ W}

Full solution

2
Useful mechanical power: $P_{\text{out}} = \eta \times P_{\text{in}} = 0.80 \times 48 = 38.4 \text{ W}$ .
3
The remaining $9.6 \text{ W}$ is lost as heat in the coils and friction.

An electric motor converts electrical energy to mechanical energy. The efficiency tells us what fraction of the input power becomes useful work; the rest is wasted as heat and friction.

Example 2

medium

A motor coil has

200

turns, area

0.01 \text{ m}^2

, carries

3 \text{ A}

, and is in a

0.5 \text{ T}

field. What is the maximum torque on the coil?

Example 3

medium

A motor coil has

50

turns, area

0.02 \text{ m}^2

, carries

4 \text{ A}

, and lies in a

0.6 \text{ T}

field. Find the maximum torque (

\tau = NBIA

Example 4

medium

A motor's single rectangular coil (

0.05 \text{ m} \times 0.1 \text{ m}

30

turns) lies parallel to a

0.5 \text{ T}

field and carries

2 \text{ A}

. Find the maximum torque.

Example 5

hard

A DC motor on

12 \text{ V}

with coil resistance

1 \Omega

runs with

2 \text{ A}

. Find the back-EMF, mechanical power, and efficiency.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

An electric drill motor operates at

240 \text{ V}

and draws

2.5 \text{ A}

. It produces a torque of

1.2 \text{ N m}

2400 \text{ rpm}

. What is the efficiency?

Example 2

hard

A DC motor has a back-EMF of

10 \text{ V}

when running at full speed. The supply voltage is

12 \text{ V}

and the coil resistance is

0.5 \text{ } \Omega

. What is the running current, the starting current (back-EMF = 0), and the mechanical power output?

Example 3

easy

A motor converts which kind of energy into which?

Example 4

easy

What force law makes a motor's coil turn?

Example 5

easy

What part reverses the current each half-turn to keep a DC motor spinning one way?

Example 6

easy

A motor wire of length

0.2

m carries

3

A in a

0.5

T field (perpendicular). Find the force.

Example 7

easy

A spinning motor also acts as a generator, producing what opposing voltage?

Example 8

easy

Is a motor the reverse process of a generator?

Example 9

easy

Doubling the current in a motor's coil does what to the force on each wire?

Example 10

easy

Why does a motor draw a large current at the instant it starts?

Example 11

medium

A motor coil has two sides each of length

0.1

m carrying

4

A in a

0.6

T field (perpendicular). Find the force on each side.

Example 12

medium

A motor coil's two sides are

0.2

m apart, each feeling

0.3

N in opposite directions. Find the torque magnitude.

Example 13

medium

A motor runs on

12

V and develops

10

V of back-EMF. The coil resistance is

1\,\Omega

. Find the current.

Example 14

medium

A motor on

24

V with

2\,\Omega

coil resistance draws

3

A while running. Find the back-EMF.

Example 15

medium

Without a commutator, what does a current loop in a magnetic field do instead of rotating continuously?

Example 16

medium

A motor draws

5

A at

100

V supply. Find the electrical power input.

Example 17

medium

A motor's force on each wire is

F=BIL

. If the field is halved and the current tripled, how does the force change?

Example 18

challenge

A motor on

120

V draws

4

A; coil resistance is

5\,\Omega

. Find the back-EMF and the mechanical power output (power minus resistive loss).

Example 19

challenge

A motor delivers torque

\tau = 0.5

N·m while spinning at

\omega = 40

rad/s. Find the mechanical power output. (

P=\tau\omega

Example 20

challenge

A single-turn rectangular coil (

0.1

m by

0.2

m) carries

5

A in a

0.4

T field, plane parallel to the field. Find the maximum torque on the coil.

Example 21

medium

A motor wire of length

0.3

m carries

5

A in a

0.4

T field (perpendicular). Find the force.

Example 22

medium

A motor on

200

V develops

160

V back-EMF with

4\,\Omega

coil resistance. Find the current.

Example 23

easy

A wire of length

0.4 \text{ m}

carries

5 \text{ A}

perpendicular to a

0.3 \text{ T}

magnetic field. Find the force on it.

Example 24

easy

A DC motor draws

6 \text{ A}

from a

24 \text{ V}

supply. What is the electrical power input?

Example 25

easy

Which rule predicts the direction of force on a motor's current-carrying wire?

Example 26

easy

Doubling the magnetic field strength in a motor does what to the force on each coil wire (current fixed)?

Example 27

medium

A motor running on

36 \text{ V}

draws

3 \text{ A}

. Its coil resistance is

2 \Omega

. Find the back-EMF.

Example 28

medium

A motor with

4 \Omega

coil resistance is connected to

24 \text{ V}

. At the instant it starts (before it spins), what is the starting current?

Example 29

medium

A motor delivers

\tau = 1.2 \text{ N} \cdot \text{m}

\omega = 50 \text{ rad/s}

. Find the mechanical power output.

Example 30

medium

A motor uses

200 \text{ W}

electrical and outputs

150 \text{ W}

mechanical. Find its efficiency.

Example 31

medium

A motor's torque is

0.4 \text{ N} \cdot \text{m}

and its shaft spins at

1200 \text{ rpm}

. Find the mechanical power output. (

1 \text{ rpm} = 2\pi/60 \text{ rad/s}

Example 32

medium

A motor on

120 \text{ V}

runs with back-EMF

108 \text{ V}

and coil resistance

0.6 \Omega

. Find the running current.

Example 33

hard

A motor with

0.5 \Omega

coil resistance runs on

12 \text{ V}

, drawing

4 \text{ A}

. Find the resistive power lost in the coil and the mechanical power output.

Example 34

hard

A motor coil with

100

turns and area

0.005 \text{ m}^2

rotates in a

0.8 \text{ T}

field while carrying

2 \text{ A}

. Find the torque when the coil's normal makes a

60^\circ

angle with the field.

Example 35

hard

A motor's input is

480 \text{ W}

. At a torque of

1.5 \text{ N} \cdot \text{m}

and angular speed

200 \text{ rad/s}

, find the efficiency.

Example 36

hard

Each side of a motor's

20

-turn rectangular coil (

0.08 \text{ m}

long) carries

3 \text{ A}

in a

0.5 \text{ T}

field perpendicular to the side. Find the force on one side of the coil (total over all turns).

Example 37

hard

A motor coil with

N

turns, area

A

, carries current

I

in field

B

. If

B

doubles and the current is halved, what happens to the maximum torque?

Example 38

hard

A motor on a

9 \text{ V}

supply runs at full speed drawing

0.5 \text{ A}

with coil resistance

1 \Omega

. Find the mechanical power output.

Example 39

hard

A motor torque of

0.8 \text{ N} \cdot \text{m}

must lift a

5 \text{ kg}

mass via a

0.04 \text{ m}

radius pulley (

g = 10 \text{ m/s}^2

). Will the motor be able to start the lift?

Example 40

challenge

A DC motor on

230 \text{ V}

has armature resistance

2 \Omega

. At full load, it draws

10 \text{ A}

. Find the back-EMF, total power input, ohmic loss, mechanical output, and efficiency.

Example 41

challenge

A motor's back-EMF is proportional to angular speed:

\varepsilon_{\text{back}} = k\omega

with

k = 0.05 \text{ V} \cdot \text{s}

. On

12 \text{ V}

with

R = 1 \Omega

, find the no-load speed (where the motor draws negligible current).

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Related Concepts

Magnetic Force Electric Current Magnetic Field

Background Knowledge

These ideas may be useful before you work through the harder examples.

magnetic forceelectric currentmagnetic field