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.
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.