Question

A generator uses a coil that has 140 turns and a 0.45-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.

Answer 1

Answer:

The length of the wire from which the coil is made is 47 m

Explanation:

Given;

number of turns, N = 140 turns

magnetic field strength, B = 0.45 T

frequency of the generator, F = 60 Hz

root mean value of emf = 120 V

Peak emf, V₀ = Vrms × √2

V₀  = 120 × √2  = 169.71 V

$L = 4\sqrt{\frac{NV_o}{B \omega}} \\\\but \ \omega = 2\pi F\\\\L = 4\sqrt{\frac{NV_o}{2\pi FB}}$

where;

L is the total length of the wire from which the coil is made

substitute the values given and solve for L

$L = 4\sqrt{\frac{NV_o}{2\pi FB}} \\\\L = 4\sqrt{\frac{140*169.71}{2\pi *60*0.45}} \ = 4\sqrt{140.035} \ = 47 m$

Therefore, the length of the wire from which the coil is made is 47 m