A generator uses a coil that has 200 turns and a 0.77-T magnetic field. The freq

Question

A generator uses a coil that has 200 turns and a 0.77-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.

A generator uses a coil that has 200 turns and a 0.77-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.

Explanation / Answer

120 Vrms = 120 * 1.414 Vpeak = 169.7 Vpeak
So the area of each coil is A = 169.7 V / (2pi * 60Hz * 500turns * 0.48T) = 0.00188 m^2
So each turn of the coil is sqrt(0.00188) m square = 0.0433 m * 0.0433 m
So the total length of wire is 4 * 0.0433 m per turn * 500 turns = 86.64 m

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