A generator uses a coil that has 140 turns and a 0.61-T magnetic field. The freq

Question

A generator uses a coil that has 140 turns and a 0.61-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 140 turns and a 0.61-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

120Vrms = 120*1.414 V peak = 169.7 Vpk

So the area of each coil is A = 169.7V / (2pi * 60Hz * 140turns * 0.61T) = 0.00527 m^2

So each turn of the coil is sqrt(.00527) m square = 0.073m * 0.073m

So the total length of wire is 4*0.073m per turn * 140 turns = 40.667 m (3 s.f.)

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