Calculating Length of Wire in a Generator Coil with Given Parameters

[cheechnchong]

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.

 

[Doc Al]

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.

 

[cheechnchong]

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?

 

[Doc Al]

What's the circumference of a square? How many squares do you have?

 

[cheechnchong]

What's the circumference of a square? How many squares do you have?

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