Electric Generators and Faraday's Law

AI Thread Summary
When a generator operates at 60 Hz, it induces an EMF of 50 V. To determine the amplitude at 180 Hz, the angular frequency (ω) is calculated as 1131 m/s. The initial attempt to find the new EMF using the sine function led to a result of 64.3 V, which was incorrect. The correct approach involves using the formula ε0 = NABω, where NAB remains constant, leading to the expected answer of 150 V. The problem was resolved by correctly applying the relationship between frequency and induced EMF.
Violagirl
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Homework Statement


When a generator turns at 60 Hz, the amplitude of the induced EMF is 50 V. What is its amplitude when it turns at 180 Hz if the magnetic field remains the same?

Homework Equations


ω = 2∏f

ε = ε0sin ωt


The Attempt at a Solution



If f = 180 Hz,

ω = 2∏(180 Hz)

ω = 1131 m/s

To find ε0 at 180 Hz:

ε/sin ωt = ε0

From this I get:

(50 V) / sin(1131 m/s)

ε0 = 64.3 V

However my book says that the answer should be 150 V and I'm not sure what I did wrong with it...
 
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50V is ε0.
ε0 = NABω. NAB doesn't change.

Solve for NAB and use that value to solve for the new ε0.
 
Thank you so much! Figured it out! :biggrin:
 
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