1. Home
  2. Physics 101
  3. Electromagnetic induction, ac
  4. Electric generators

16.4 Electric generators  (Page 2/6)

<< Chapter < Page
  Physics 101     Page 2 / 6
Chapter >> Page >
emf = 2 Bℓ w 2 ω sin ωt = ( ℓ w ) Bω 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 = ℓ 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 / 2π size 12{f=ω/2π} {} , and the period is T = 1 / f = 2π / 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 = 2π / 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 does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
What are the treatment for autism?
Magret Reply
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision. play therapy. speech therapy. Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game. string and beads game. the more you interact with the child the more effective
Jharna
results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.
Jharna
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 3

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Physics 101' conversation and receive update notifications?

Ask