The electric generator

In summary, the peak emf of a generator with a coil radius of 0.14 m, length of 5.4 m, magnetic field of 0.10 T, and angular speed of 35 rad/s can be calculated using Faraday's law and the formula for induced EMF. The number of loops and the area of the coil must also be considered in the calculation.
  • #1
mayo2kett
23
0
The coil of a generator has a radius of 0.14 m. When this coil is unwound, the wire from which it is made has a length of 5.4 m. The magnetic field of the generator is 0.10 T, and the coil rotates at an angular speed of 35 rad/s. What is the peak emf of this generator?

so i have:
r= .14m
L= 5.4m
B= .10T
w=35 rad/s

now i thought i would do:
emf= BLv
v=rw... v= .14m(35 rad/s)
emf= (.10T)(5.4m)(.049m/s)= .02646
and peak emf= (square root 2)(emf)= .0374...

this problem is wrong the way i tried it, but I'm not sure what i should do differently
 
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  • #2
mayo2kett said:
The coil of a generator has a radius of 0.14 m. When this coil is unwound, the wire from which it is made has a length of 5.4 m. The magnetic field of the generator is 0.10 T, and the coil rotates at an angular speed of 35 rad/s. What is the peak emf of this generator?

so i have:
r= .14m
L= 5.4m
B= .10T
w=35 rad/s

now i thought i would do:
emf= BLv
v=rw... v= .14m(35 rad/s)
emf= (.10T)(5.4m)(.049m/s)= .02646
and peak emf= (square root 2)(emf)= .0374...

this problem is wrong the way i tried it, but I'm not sure what i should do differently

The induced EMF (across the ends of the rod) due to the motion of a rod of length 'l' and velocity 'v', in the presence of a magnetic field of strength 'B' is Blv. So this formula is not applicable here as there is a rotating coil and not a rod.

To solve this problem, go from the definition of Farady's law.
By Farady's law, Emf induced = -d(Magnetic Flux)/dt

Let the magnetic field make an angle theta with the area vector of the loop at any time 't' such that at t=0, theta=0.
So the Magnetic flux enclosed by the loop is = [itex] n B.A [/itex]
where n is the number of loops, B is the magnetic field and A is the area of the loop.

[tex] = (n)(B)(A)(\cos\theta) [/tex]

So, the EMF induced will be

[tex] =\frac {-d[(n)(B)(A)(\cos\theta)]}{dt} [/tex]

From this, can you calculate the EMF as a function of time and from that the peak value?
(You will have to find the relation between 'theta' and 't' as well as the value of n)
 
Last edited:
  • #3
The coil is rotating in the field. The flux is thus changing and this causes the electric field in the coil.

[tex] \Phi = AB [/tex], B is constant but A is changing. Can you find A as a function of time?

[tex] E = -N \frac{d\Phi}{dt} [/tex], so you will also need to find N - the number of layers in the coil.

Just find [tex] \frac{dA}{dt}[/tex] and the biggest problem is probably solved.
 
  • #4
thanks guys... you really helped me
 

1. How does an electric generator work?

An electric generator works by converting mechanical energy into electrical energy. This is done through a process called electromagnetic induction, where a coil of wire is rotated between the poles of a magnet. This rotation causes the wire to cut through the magnetic field, creating an electric current.

2. What are the main components of an electric generator?

The main components of an electric generator include the rotor (rotating part), stator (stationary part), and the electromagnetic field. The rotor contains the coil of wire, while the stator houses the magnets. The electromagnetic field is created by the interaction between the rotor and stator.

3. What are the different types of electric generators?

There are several types of electric generators, including AC generators, DC generators, and induction generators. AC generators use alternating current, while DC generators use direct current. Induction generators use the principles of electromagnetic induction to generate electricity.

4. What are the main uses of electric generators?

Electric generators are commonly used to provide backup power during outages, as well as to power remote or off-grid locations. They are also used in large-scale power plants to generate electricity for cities and communities.

5. How efficient are electric generators?

The efficiency of electric generators can vary, with most modern generators achieving an efficiency of around 95%. Factors that can affect efficiency include the type of generator, the quality of its components, and the conditions under which it is used. Regular maintenance and proper usage can help improve efficiency.

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