Generator Examples in Physics

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 5050 turns, area 0.04 m20.04 \text{ m}^2, rotating in a 0.5 T0.5 \text{ T} magnetic field. What is the peak EMF if the coil rotates at 60 Hz60 \text{ Hz}?

Answer

E0=377 V\mathcal{E}_0 = 377 \text{ V}

First step

1
Peak EMF for a generator: E0=NABω\mathcal{E}_0 = NAB\omega, where ω=2πf\omega = 2\pi f.

Full solution

  1. 2
    Angular frequency: ω=2π×60=377 rad/s\omega = 2\pi \times 60 = 377 \text{ rad/s}.
  2. 3
    E0=50×0.04×0.5×377=377 V\mathcal{E}_0 = 50 \times 0.04 \times 0.5 \times 377 = 377 \text{ 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 V170 \text{ V} at 50 Hz50 \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=80N=80 turns, area A=0.02 m2A=0.02\text{ m}^2, in a field B=0.6 TB=0.6\text{ T}, and spins at f=60 Hzf=60\text{ Hz}. Find the peak EMF.

Example 4

medium
A generator coil N=40N=40, A=0.05 m2A=0.05\text{ m}^2, B=0.3 TB=0.3\text{ T} spins at ω=100 rad/s\omega=100\text{ rad/s}. Find the instantaneous EMF at the moment ωt=60°\omega t = 60°.

Example 5

hard
A coil generator has N=50N=50, A=0.06 m2A=0.06\text{ m}^2, B=0.5 TB=0.5\text{ T}. What rotation rate (in Hz) is needed to produce 120 V120\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 100100 turns and area 0.05 m20.05 \text{ m}^2 in a 0.4 T0.4 \text{ T} field. It needs to produce a peak EMF of 500 V500 \text{ V}. At what frequency must it rotate?

Example 2

hard
A hydroelectric generator produces 10 MW10 \text{ MW} at 20,000 V20{,}000 \text{ V} RMS. What RMS current does it deliver? If the transmission line has 2 Ω2 \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=10N=10, B=0.5B=0.5 T, A=0.2A=0.2 m2^2, ω=4\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=50N=50, B=0.4B=0.4 T, A=0.1A=0.1 m2^2, ω=10\omega=10 rad/s. Find the peak EMF.

Example 12

medium
A generator's peak EMF is 100100 V. What is the RMS voltage? (Vrms=Vpeak/2V_{rms}=V_{peak}/\sqrt2.)

Example 13

medium
A generator should produce 2424 V peak with B=0.6B=0.6 T, A=0.2A=0.2 m2^2, ω=10\omega=10 rad/s. Find the number of turns.

Example 14

medium
A generator coil has area 0.050.05 m2^2, N=100N=100, ω=20\omega=20 rad/s, peak EMF 4040 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 5050 Hz AC. Find the angular speed ω\omega. (ω=2πf\omega = 2\pi f.)

Example 17

challenge
A generator coil N=200N=200, area 0.040.04 m2^2, in B=0.5B=0.5 T spins at 5050 Hz. Find the peak EMF.

Example 18

challenge
A generator delivers 120120 V RMS to a 10 Ω10\,\Omega load. Find the average power dissipated. (P=Vrms2/RP = V_{rms}^2/R.)

Example 19

challenge
A generator coil spins at ω=30\omega=30 rad/s with peak EMF 9090 V into a 30 Ω30\,\Omega resistor. Find the peak current and the instantaneous EMF at tt when ωt=30°\omega t = 30°. (sin⁡30°=0.5\sin30°=0.5.)

Example 20

medium
A coil: N=20N=20, B=0.5B=0.5 T, A=0.3A=0.3 m2^2, ω=5\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 170170 V. Find its RMS voltage. (Vrms=Vpeak/2V_{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=25N=25, B=0.2 TB=0.2\text{ T}, A=0.1 m2A=0.1\text{ m}^2 rotates at ω=8 rad/s\omega=8\text{ rad/s}. Find the peak EMF.

Example 25

easy
A generator rotates at f=25 Hzf = 25\text{ Hz}. Find its angular frequency ω\omega.

Example 26

medium
A generator must produce a peak EMF of 200 V200\text{ V}. Given B=0.5 TB=0.5\text{ T}, A=0.04 m2A=0.04\text{ m}^2, ω=100 rad/s\omega = 100\text{ rad/s}, find the required number of turns.

Example 27

medium
A generator outputs Epeak=150 V\mathcal{E}_{peak} = 150\text{ V}. What is its RMS voltage?

Example 28

medium
A generator's instantaneous EMF is E(t)=170sin⁡(120πt) V\mathcal{E}(t) = 170\sin(120\pi t)\text{ V}. What is the frequency?

Example 29

medium
If you double both the area AA and the angular speed ω\omega of a generator coil, by what factor does the peak EMF change?

Example 30

medium
A generator coil with peak EMF 80 V80\text{ V} drives a 20 Ω20\,\Omega resistor. Find the peak current and RMS power dissipated.

Example 31

medium
A bicycle dynamo generator produces 6 V6\text{ V} peak at 30 km/h30\text{ km/h}. Assuming peak EMF is proportional to wheel speed, what peak EMF is produced at 20 km/h20\text{ km/h}?

Example 32

hard
A power-station generator produces 25 kV25\text{ kV} RMS at 50 Hz50\text{ Hz}. If the coil has N=500N=500 turns in B=1.2 TB=1.2\text{ T}, find the coil area.

Example 33

hard
A generator delivers 20 A20\text{ A} RMS at 240 V240\text{ V} RMS. What mechanical power must drive it if the generator is 90%90\% efficient?

Example 34

hard
A wind-turbine generator rotates at ω=12 rad/s\omega = 12\text{ rad/s} with N=300N=300, B=0.8 TB=0.8\text{ T}, A=1.5 m2A=1.5\text{ m}^2. Find the average power dissipated in a 50 Ω50\,\Omega load.

Example 35

hard
An AC generator's coil normal makes angle θ=ωt\theta = \omega t with B⃗\vec B. Show why the EMF magnitude is NBAω∣sin⁡(ωt)∣NBA\omega|\sin(\omega t)|, not cos⁡\cos.

Example 36

hard
A generator coil drives a 40 Ω40\,\Omega load with Vrms=110 VV_{rms} = 110\text{ V}. The coil + connecting wires have internal resistance 5 Ω5\,\Omega. Find the load's average power.

Example 37

challenge
A generator delivers 5 kW5\text{ kW} at 250 V250\text{ V} RMS through a 1 Ω1\,\Omega transmission line. By what factor does line loss change if the same power is sent at 2500 V2500\text{ V} RMS?

Example 38

medium
A 4-pole AC generator rotates mechanically at fmech=30 Hzf_{mech} = 30\text{ Hz}. What electrical frequency does it produce? (felec=(pole pairs)fmechf_{elec} = (\text{pole pairs}) f_{mech}.)
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Background Knowledge

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

faradays lawlenzs law