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A generator uses a coil that has 110 turns and a 0.42-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 :

Answer:

44 m.

Explanation:

Given,

Number of turns, N = 110 turns

Magnetic field, B = 0.42 T

frequency, f = 60 Hz

emf rms value = 120 V

Now, Peak emf calculation

[tex]\epsilon_0 = \sqrt{2} \epsilon[/tex]

[tex]\epsilon_0 = \sqrt{2}\times 120[/tex]

[tex]\epsilon_0 = 170\ V[/tex]

Now, Total length calculation

[tex]L = 4\sqrt{\dfrac{N\epsilon_0}{B\omega}}[/tex]

[tex]L =4 \sqrt{\dfrac{N\epsilon_0}{B(2\pi f)}}[/tex]

[tex]L =4\times \sqrt{\dfrac{110\times 170}{0.42\times (2\pi\times 60)}}[/tex]

L = 44 m(approx.)

Length of the coil is equal to 44 m.

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