Electric Generator Problem

In summary, the generator has a length of .931 m from a wire made of 100 turns of a coil with a 0.50-T magnetic field.
  • #1
132
1

Homework Statement



A generator uses a coil that has 100 turns and a 0.50-T magnetic field. The frequency of this generator is 60.0 Hz, and its emf has an rms value of 120 V. Assuming that each turn of the coil is a square (an approximation), determine the length of the wire from which the coil is made.

Homework Equations



Emf = NABwsin(wt) -- not sure if i should utilize sin(wt)?

and w = 2(pi)f

The Attempt at a Solution



I notice that the problem includes emf as an rms value. I figure that it is sq(2). Then, I figure out the w - the value is 377.

The problem setup so far is...

sq(2)*120V = (100 turns)(A)(0.50-T)(377) sin (377*.02) ---- i figured time, t by using the frequency T = 1/f equation.

Solving for A, I get A = .069 m^2. I then solve for the radius using A = (pi)r^2 and get r = .148 m. Then, I plug the r into L = 2(pi)r to get length. My answer is L = .931 m (final answer).


Book Answer: 38 m

Now the answer I was given doesn't match with what i was given. I am guessing whether I should multiply by 100 since there are that many turns in the coil? Or just ignore the sin(wt) part? I just don't know how to fix this problem. My book does a horrible job explaining how to approach generator problems.
 
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  • #2
cheechnchong said:

Homework Equations



Emf = NABwsin(wt) -- not sure if i should utilize sin(wt)?
That equation will give you the instantaneous Emf--but you need the RMS value. Big hint: Replace sin(wt) by 1/sq(2).

The problem setup so far is...

sq(2)*120V = (100 turns)(A)(0.50-T)(377) sin (377*.02) ---- i figured time, t by using the frequency T = 1/f equation.
Get rid of that sin(wt) term and your value for time.

Solving for A, I get A = .069 m^2. I then solve for the radius using A = (pi)r^2 and get r = .148 m. Then, I plug the r into L = 2(pi)r to get length. My answer is L = .931 m (final answer).
It's a square, not a circle.

Now the answer I was given doesn't match with what i was given. I am guessing whether I should multiply by 100 since there are that many turns in the coil?
Of course--you want the total length of the wire.

Or just ignore the sin(wt) part? I just don't know how to fix this problem.
See my comments above.
 
  • #3
I used the equation E = NABw(1/sq(2)). I solved for w using w = 2(pi)f. Plugged all the values into the equation and got A = .009 m^2.

This is where I'm stuck...After solving for the side of the square A = s^2 using .009 m^2 (area that was figured), I came up with s = .095 m. How can I figure the L-value? I'm STUCK here!

What's the fix there doc?
 
  • #4
What's the circumference of a square? How many squares do you have?
 
  • #5
Doc Al said:
What's the circumference of a square? How many squares do you have?

Doc Al, you are awesome! worked out just fine...
 

1. How does an electric generator work?

An electric generator works by converting mechanical energy into electrical energy. This is done through the use of a magnet and a coil of wire. When the coil of wire is rotated within the magnetic field, it creates an electric current.

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

The main components of an electric generator include a rotor, stator, and an external power source. The rotor is the rotating part of the generator, while the stator is the stationary part. The external power source is used to turn the rotor and create the mechanical energy needed for the generator to work.

3. What is the difference between an AC and DC generator?

An AC (alternating current) generator produces an alternating current, meaning the direction of the current changes periodically. A DC (direct current) generator produces a direct current, which means the current flows in one direction. AC generators are more commonly used in power plants, while DC generators are used in smaller devices like batteries.

4. What are some common problems with electric generators?

Some common problems with electric generators include low fuel levels, damaged or worn out parts, and electrical problems such as short circuits. Low fuel levels can lead to the generator not producing enough power, while damaged parts can cause the generator to malfunction. Electrical problems can also cause the generator to fail or not function properly.

5. How can I troubleshoot an electric generator problem?

If you are experiencing issues with your electric generator, some troubleshooting steps you can take include checking the fuel levels, inspecting the parts for damage, and testing the electrical components. It is also important to refer to the manufacturer's manual for specific troubleshooting steps and seek professional help if needed.

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