Electric Generators and Faraday's Law

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SUMMARY

The discussion focuses on calculating the amplitude of induced EMF in an electric generator when the frequency changes from 60 Hz to 180 Hz, while maintaining a constant magnetic field. The initial amplitude of the induced EMF is 50 V at 60 Hz. Using the formula ε = NABω, the correct amplitude at 180 Hz is determined to be 150 V, correcting the initial miscalculation of 64.3 V. The key takeaway is that the amplitude of induced EMF is directly proportional to the frequency when other factors remain constant.

PREREQUISITES
  • Understanding of Faraday's Law of Electromagnetic Induction
  • Familiarity with the relationship between frequency and angular velocity (ω = 2∏f)
  • Knowledge of the formula for induced EMF (ε = NABω)
  • Basic trigonometry for sine functions
NEXT STEPS
  • Study the principles of Faraday's Law in greater detail
  • Learn about the effects of changing frequency on electromagnetic induction
  • Explore the relationship between magnetic flux and induced EMF
  • Investigate practical applications of electric generators in various industries
USEFUL FOR

Students studying physics, electrical engineering professionals, and anyone interested in the principles of electromagnetic induction and electric generator design.

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...
 
Physics news on Phys.org
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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