The coil in a 60-Hz ac generator has 125 turns, each having an area of 3.0 * 10-2 m2 and is rotated in a uniform 0.12-T magnetic field. What is the peak output voltage of this generator?

Answer: 169.67 V

Explanation:

From Faraday's Law, we know that

emf = - d (magnetic flux) / d t

magnetic flux = N B A cos (θ), where

N = number of turns

B = magnetic field

A = area of coils

cos (θ) = results from dot product of magnetic field vector and area vector.

θ = a function of time as the coil is rotating.

emf = N B A (2πf) sin (2π f t)

f = frequency

sin 2πft = 1

The peak output voltage is then

emf = (125) * (0.12) * (3*10^-2) * (2 * 3.142 * 60)

emf = 0.45 * 377.04

emf = 169.67 V

Given that,.

Frequency

f = 60Hz

Number of turns

N = 125turns

Surface area of coil

A = 3 * 10^-2 m²

Magnetic field

B = 0.12T

Voltage peak to peak? I. e the EMF

EMF is given as

ε = - dΦ/dt

Where Φ is magnetic flux and it is given as

Φ = NBA Cosθ

Where N is number of turns

B is magnetic field

A is the cross sectional area

And θ is the resulting angle from the dot product of area and magnetic field

Where θ = ωt and ω = 2πf

Then, θ = 2πft

So, your magnetic flux becomes

Φ = NBA Cos (2πft)

Now, dΦ / dt = - NBA•2πf Sin (2πft)

dΦ / dt = - 2πf • NBA Sin (2πft)

So, ε = - dΦ/dt

Then,

ε = 2πf • NBA Sin (2πft)

So, the maximum peak to peak emf will occur when the sine function is 1

I. e Sin (2πft) = 1

So, the required peak to peak emf is

ε = 2πf • NBA

Substituting all the given parameters

ε = 2π * 60 * 125 * 0.12 * 3 * 10^-2

ε = 169.65 Volts

The peak to peak voltage is 169.65 V