Generator Examples: 43 Problems with Answers

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

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 mechanical (kinetic) energy into electrical energy by rotating a coil of wire within a magnetic field, exploiting electromagnetic induction.

Spin a loop of wire between magnets and you get electricity — the changing flux induces a voltage that drives current through an external circuit.

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: Generator 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 generator 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 simple AC generator has a coil of

50

turns, area

0.04 \text{ m}^2

, rotating in a

0.5 \text{ T}

magnetic field. What is the peak EMF if the coil rotates at

60 \text{ Hz}

Answer

E_{0} = 377 V

First step

Peak EMF for a generator:

\mathcal{E}_0 = NAB\omega

, where

\omega = 2\pi f

Full solution

2
Angular frequency: $\omega = 2\pi \times 60 = 377 \text{ rad/s}$ .
3
$E_{0} = 50 \times 0.04 \times 0.5 \times 377 = 377 V$

An AC generator converts mechanical energy to electrical energy by rotating a coil in a magnetic field. The peak EMF increases with more turns, larger area, stronger field, and faster rotation.

Example 2

medium

A generator produces a peak EMF of

170 \text{ V}

50 \text{ Hz}

. What is the RMS voltage? What frequency is used in the power grid in most countries?

Example 3

medium

A generator coil has

N=80

turns, area

A=0.02\text{ m}^2

, in a field

B=0.6\text{ T}

, and spins at

f=60\text{ Hz}

. Find the peak EMF.

Example 4

medium

A generator coil

N=40

A=0.05\text{ m}^2

B=0.3\text{ T}

spins at

\omega=100\text{ rad/s}

. Find the instantaneous EMF at the moment

\omega t = 60°

Example 5

hard

A coil generator has

N=50

A=0.06\text{ m}^2

B=0.5\text{ T}

. What rotation rate (in Hz) is needed to produce

120\text{ V}

RMS?

Practice Problems

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

Example 1

medium

A generator coil has

100

turns and area

0.05 \text{ m}^2

in a

0.4 \text{ T}

field. It needs to produce a peak EMF of

500 \text{ V}

. At what frequency must it rotate?

Example 2

hard

A hydroelectric generator produces

10 \text{ MW}

20{,}000 \text{ V}

RMS. What RMS current does it deliver? If the transmission line has

2 \text{ } \Omega

resistance, what percentage of power is lost in transmission?

Example 3

easy

A generator converts which kind of energy into electrical energy?

Example 4

easy

What type of current does a simple rotating-coil generator naturally produce?

Example 5

easy

Write the peak EMF formula for a rotating-coil generator.

Example 6

easy

A coil:

N=10

B=0.5

A=0.2

^2

\omega=4

rad/s. Find the peak EMF.

Example 7

easy

Does a generator create energy from nothing?

Example 8

easy

What spins the coil in a hydroelectric generator?

Example 9

easy

Doubling the rotation speed of a generator does what to the peak EMF?

Example 10

easy

A generator with a commutator (split-ring) produces what kind of current?

Example 11

medium

A coil:

N=50

B=0.4

A=0.1

^2

\omega=10

rad/s. Find the peak EMF.

Example 12

medium

A generator's peak EMF is

100

V. What is the RMS voltage? (

V_{rms}=V_{peak}/\sqrt2

Example 13

medium

A generator should produce

24

V peak with

B=0.6

A=0.2

^2

\omega=10

rad/s. Find the number of turns.

Example 14

medium

A generator coil has area

0.05

^2

N=100

\omega=20

rad/s, peak EMF

40

V. Find the field strength.

Example 15

medium

Why does a generator coil produce zero EMF at the instant its plane is perpendicular to the field?

Example 16

medium

A generator outputs

50

Hz AC. Find the angular speed

\omega

. (

\omega = 2\pi f

Example 17

challenge

A generator coil

N=200

, area

0.04

^2

, in

B=0.5

T spins at

50

Hz. Find the peak EMF.

Example 18

challenge

A generator delivers

120

V RMS to a

10\,\Omega

load. Find the average power dissipated. (

P = V_{rms}^2/R

Example 19

challenge

A generator coil spins at

\omega=30

rad/s with peak EMF

90

V into a

30\,\Omega

resistor. Find the peak current and the instantaneous EMF at

t

when

\omega t = 30°

. (

\sin30°=0.5

Example 20

medium

A coil:

N=20

B=0.5

A=0.3

^2

\omega=5

rad/s. Find the peak EMF.

Example 21

medium

Tripling the number of turns of a generator coil does what to the peak EMF?

Example 22

medium

A generator's peak EMF is

170

V. Find its RMS voltage. (

V_{rms}=V_{peak}/\sqrt2

Example 23

easy

Name the physical principle a generator relies on to convert mechanical motion into an EMF.

Example 24

easy

A coil with

N=25

B=0.2\text{ T}

A=0.1\text{ m}^2

rotates at

\omega=8\text{ rad/s}

. Find the peak EMF.

Example 25

easy

A generator rotates at

f = 25\text{ Hz}

. Find its angular frequency

\omega

Example 26

medium

A generator must produce a peak EMF of

200\text{ V}

. Given

B=0.5\text{ T}

A=0.04\text{ m}^2

\omega = 100\text{ rad/s}

, find the required number of turns.

Example 27

medium

A generator outputs

\mathcal{E}_{peak} = 150\text{ V}

. What is its RMS voltage?

Example 28

medium

A generator's instantaneous EMF is

\mathcal{E}(t) = 170\sin(120\pi t)\text{ V}

. What is the frequency?

Example 29

medium

If you double both the area

A

and the angular speed

\omega

of a generator coil, by what factor does the peak EMF change?

Example 30

medium

A generator coil with peak EMF

80\text{ V}

drives a

20\,\Omega

resistor. Find the peak current and RMS power dissipated.

Example 31

medium

A bicycle dynamo generator produces

6\text{ V}

peak at

30\text{ km/h}

. Assuming peak EMF is proportional to wheel speed, what peak EMF is produced at

20\text{ km/h}

Example 32

hard

A power-station generator produces

25\text{ kV}

RMS at

50\text{ Hz}

. If the coil has

N=500

turns in

B=1.2\text{ T}

, find the coil area.

Example 33

hard

A generator delivers

20\text{ A}

RMS at

240\text{ V}

RMS. What mechanical power must drive it if the generator is

90\%

efficient?

Example 34

hard

A wind-turbine generator rotates at

\omega = 12\text{ rad/s}

with

N=300

B=0.8\text{ T}

A=1.5\text{ m}^2

. Find the average power dissipated in a

50\,\Omega

load.

Example 35

hard

An AC generator's coil normal makes angle

\theta = \omega t

with

\vec B

. Show why the EMF magnitude is

NBA\omega|\sin(\omega t)|

, not

\cos

Example 36

hard

A generator coil drives a

40\,\Omega

load with

V_{rms} = 110\text{ V}

. The coil + connecting wires have internal resistance

5\,\Omega

. Find the load's average power.

Example 37

challenge

A generator delivers

5\text{ kW}

250\text{ V}

RMS through a

1\,\Omega

transmission line. By what factor does line loss change if the same power is sent at

2500\text{ V}

RMS?

Example 38

medium

A 4-pole AC generator rotates mechanically at

f_{mech} = 30\text{ Hz}

. What electrical frequency does it produce? (

f_{elec} = (\text{pole pairs}) f_{mech}

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Related Concepts

Faraday's Law Lenz's Law Transformer

Background Knowledge

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

faradays lawlenzs law