How fast must the rotor of a generator rotate?

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Homework Help Overview

The problem involves determining the rotational speed required for a generator's rotor to achieve a specific maximum induced electromotive force (emf). The context is within the subject area of electromagnetism, specifically focusing on the principles of induced emf in generators.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the induced emf and the rotational speed of the rotor, referencing the formula for induced emf. Some express concerns about insufficient information, particularly regarding the magnetic field strength. Others explore the implications of using different formulas for induced emf and the conditions under which they apply.

Discussion Status

There is an ongoing exploration of the formulas related to induced emf, with participants providing different perspectives on how to approach the problem. Some guidance has been offered regarding the use of the maximum value of the sine function in the context of the equations, and there is a suggestion to maintain consistency in the parameters used across calculations.

Contextual Notes

Participants note the absence of specific values for the magnetic field strength and the area of the coil, which are critical for solving the problem. There is also mention of the need to convert units appropriately, although some suggest that this may not be necessary for the calculations at hand.

xswtxoj
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Homework Statement


The maximum indicued emf in a generator is 205rpm is 43.0V. How fast must the rotor of the generator rotate if it's to generate a maximum inducded emf of 55.0V?

Homework Equations


E= NBAsinwt

The Attempt at a Solution


205r/m*2 (Pi)/ 1rev81min/60s = 21.46rad/s
magnet field isn't given, so how can u solve this?
 
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Check the formula for induced emf.
 


i did, but ur not given enough info to solve it, when u have E=-N ( magnetic flux)/ time or motion emf which is E= Blv
 


Formula for induces emf is E = NBAwsin(wt)
 


xswtxoj said:
i did, but ur not given enough info to solve it, when u have E=-N ( magnetic flux)/ time or motion emf which is E= Blv

When a coil is moving in a magnetic field, E = -N( change in magnetic flux/time)
When a conductor is moving a magnetic field with a velocity v, E = Blv.
In your problem you hve to the first formula. At any instant th magnetic flux = NBA*cos(wt)
 


The eq for the induced emf is NBAwsin(wt). To max this eq out you have to realize the max value for the sin function is 1. Therefore, the max emf = NBAw. Since they give you what the max emf is for an w=205rev/min, you can simply solve for a value of (NBA). and use this same value for (NBA) in the eq 55V=(NBA)(w). You have to realize that the values for N, B, and A are not changing for this situation. You do not really have to change the w to SI units, or, 21.46 rad/sec. You can use the 205 rev/ min as the w to find a value for (NBA) and plug this into the eq 55V = (NBA)(w). Either way you get approx 262 rev/min.
 

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