How Do You Calculate the Length of Wire in a Generator Coil?

[thompson.1674]

Homework Statement

A generator uses a coil that has 80 turns and a 0.35 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

E=NABwsinwt
w=2pif

The Attempt at a Solution

Vpeak=sqrt2 * 120= 169.71
w=2pi(60)=376.99
169.71=80*A*.35*376.99*(sin367.99*t)
but where do i go from here?

 

[thompson.1674]

nevermind i got it

 

[baba89]

I would suggest starting by simplifying the equation and solving for the length of the wire. First, we can rewrite the equation using the given values:

Vpeak = NABwsinwt

Since we are trying to find the length of the wire (represented by A), we can rearrange the equation to isolate A:

A = Vpeak / (NBwsinwt)

Next, we can substitute in the given values:

A = 169.71 / (80 * 0.35 * 376.99 * sin(367.99*t))

Now, we can simplify the equation by using the fact that each turn of the coil is square, meaning that the length and width are equal. Therefore, we can assume that the length of the wire is equal to the width of the coil, and we can substitute in the number of turns (N) for the width (w):

A = 169.71 / (80 * 0.35 * 376.99 * sin(367.99*t)) = 0.000000188

This gives us the length of the wire per turn. To find the total length of the wire, we need to multiply by the number of turns (N):

Total length of wire = 80 * 0.000000188 = 0.00001504 meters

Therefore, the length of the wire from which the coil is made is approximately 0.00001504 meters.