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emf = 2 Bℓ w 2 ω sin ωt = ( w ) sin ωt . size 12{"emf"=2Bℓ { {w} over {2} } ω"sin"ωt= \( ℓw \) Bω"sin"ωt} {}

Noting that the area of the loop is A = w size 12{A=ℓw} {} , and allowing for N size 12{N} {} loops, we find that

emf = NAB ω sin ωt size 12{"emf"= ital "NAB"ω"sin"ωt} {}

is the emf induced in a generator coil    of N size 12{N} {} turns and area A size 12{A} {} rotating at a constant angular velocity ω in a uniform magnetic field B size 12{B} {} . This can also be expressed as

emf = emf 0 sin ωt , size 12{"emf"="emf" rSub { size 8{0} } "sin"ωt} {}

where

emf 0 = NAB ω size 12{"emf" rSub { size 8{0} } = ital "NAB"ω} {}

is the maximum (peak) emf . Note that the frequency of the oscillation is f = ω / size 12{f=ω/2π} {} , and the period is T = 1 / f = / ω size 12{T=1/f=2π/ω} {} . [link] shows a graph of emf as a function of time, and it now seems reasonable that AC voltage is sinusoidal.

The first part of the figure shows a schematic diagram of a single coil electric generator. It consists of a rotating rectangular loop placed between the two poles of a permanent magnet shown as two rectangular blocks curved on side facing the loop. The magnetic field B is shown pointing from the North to the South Pole. The two ends of this loop are connected to the two small rings. The two conducting carbon brushes are kept pressed separately on both the rings. The loop is rotated in the field with an angular velocity omega. Outer ends of the two brushes are connected to an electric bulb which is shown to glow brightly. The second part of the figure shows the graph for e m f generated E as a function of time t. The e m f is along the Y axis and the time t is along the X axis. The graph is a progressive sine wave with a time period T. The crest maxima are at E zero and trough minima are at negative E zero.
The emf of a generator is sent to a light bulb with the system of rings and brushes shown. The graph gives the emf of the generator as a function of time. emf 0 size 12{"emf" rSub { size 8{0} } } {} is the peak emf. The period is T = 1 / f = / ω size 12{T=1/f=2π/ω} {} , where f size 12{f} {} is the frequency. Note that the script E stands for emf.

The fact that the peak emf, emf 0 = NAB ω size 12{"emf" rSub { size 8{0} } = ital "NAB"ω} {} , makes good sense. The greater the number of coils, the larger their area, and the stronger the field, the greater the output voltage. It is interesting that the faster the generator is spun (greater ω size 12{ω} {} ), the greater the emf. This is noticeable on bicycle generators—at least the cheaper varieties. One of the authors as a juvenile found it amusing to ride his bicycle fast enough to burn out his lights, until he had to ride home lightless one dark night.

[link] shows a scheme by which a generator can be made to produce pulsed DC. More elaborate arrangements of multiple coils and split rings can produce smoother DC, although electronic rather than mechanical means are usually used to make ripple-free DC.

The first part of the figure shows a schematic diagram of a single coil D C electric generator. It consists of a rotating rectangular loop placed between the two poles of a permanent magnet shown as two rectangular blocks curved on side facing the loop. The magnetic field B is shown pointing from the North to the South Pole. The two ends of this loop are connected to the two sides of a split ring. The two conducting carbon brushes are kept pressed separately on both sides of the split rings. The loop is rotated in the field with an angular velocity w. Outer ends of the two brushes are connected to an electric bulb which is shown to glow brightly. The second part of the figure shows the graph for e m f generated as a function of time. The e m f is along the Y axis and the time t is along the X axis. The graph is a progressive and rectified sine wave with a time period T. The sine wave has only positive pulses. The crest maxima are at E zero.
Split rings, called commutators, produce a pulsed DC emf output in this configuration.

Calculating the maximum emf of a generator

Calculate the maximum emf, emf 0 size 12{"emf" rSub { size 8{0} } } {} , of the generator that was the subject of [link] .

Strategy

Once ω size 12{ω} {} , the angular velocity, is determined, emf 0 = NAB ω size 12{"emf" rSub { size 8{0} } = ital "NAB"ω} {} can be used to find emf 0 size 12{"emf" rSub { size 8{0} } } {} . All other quantities are known.

Solution

Angular velocity is defined to be the change in angle per unit time:

ω = Δ θ Δ t . size 12{ω= { {Δθ} over {Δt} } } {}

One-fourth of a revolution is π/2 size 12{l} {} radians, and the time is 0.0150 s; thus,

ω = π / 2 rad 0.0150 s = 104 . 7 rad/s .

104.7 rad/s is exactly 1000 rpm. We substitute this value for ω size 12{ω} {} and the information from the previous example into emf 0 = NAB ω size 12{"emf" rSub { size 8{0} } = ital "NAB"ω} {} , yielding

emf 0 = NAB ω = 200 ( 7 . 85 × 10 3 m 2 ) ( 1 . 25 T ) ( 104 . 7 rad/s ) = 206 V . alignl { stack { size 12{"emf" rSub { size 8{0} } = ital "NAB"ω} {} #" "="200" \( 7 "." "85" times "10" rSup { size 8{ - 3} } " m" rSup { size 8{2} } \) \( 1 "." "25"" T" \) \( "104" "." 7" rad/s" \) {} # " "="206"" V" {}} } {}

Discussion

The maximum emf is greater than the average emf of 131 V found in the previous example, as it should be.

In real life, electric generators look a lot different than the figures in this section, but the principles are the same. The source of mechanical energy that turns the coil can be falling water (hydropower), steam produced by the burning of fossil fuels, or the kinetic energy of wind. [link] shows a cutaway view of a steam turbine; steam moves over the blades connected to the shaft, which rotates the coil within the generator.

Photograph of a steam turbine connected to a generator.
Steam turbine/generator. The steam produced by burning coal impacts the turbine blades, turning the shaft which is connected to the generator. (credit: Nabonaco, Wikimedia Commons)

Generators illustrated in this section look very much like the motors illustrated previously. This is not coincidental. In fact, a motor becomes a generator when its shaft rotates. Certain early automobiles used their starter motor as a generator. In Back Emf , we shall further explore the action of a motor as a generator.

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, College physics -- hlca 1104. OpenStax CNX. May 18, 2013 Download for free at http://legacy.cnx.org/content/col11525/1.1
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