How fast must the rotor of a generator rotate?

In summary, the problem asks for the required rotor speed of a generator to generate a maximum induced emf of 55.0V, given the maximum induced emf at 205rpm is 43.0V. Using the formula E = NBAwsin(wt), we can solve for (NBA) and plug it into the equation 55V = (NBA)(w) to find the required rotor speed to be approximately 262 rev/min.
  • #1
xswtxoj
87
0

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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  • #2


Check the formula for induced emf.
 
  • #3


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
 
  • #4


Formula for induces emf is E = NBAwsin(wt)
 
  • #5


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)
 
  • #6


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.
 

1. What is the ideal speed for a generator rotor to rotate at?

The ideal speed for a generator rotor to rotate at depends on the design of the specific generator. Generally, most generators operate at speeds between 1,000 and 3,600 rotations per minute (RPM). However, some generators may have different speed requirements depending on their intended use.

2. How does the speed of the rotor affect the output of the generator?

The speed of the rotor directly affects the output of the generator. A faster rotating rotor will produce more electricity, while a slower rotating rotor will produce less. This is because the rotational speed determines the frequency of the electric current produced by the generator.

3. Can a generator rotor rotate too fast?

Yes, a generator rotor can rotate too fast. If the rotor rotates at a speed higher than its designed limit, it can cause overheating and damage to the generator. This can also lead to a decrease in the lifespan of the generator.

4. What factors determine the required speed for a generator rotor?

The required speed for a generator rotor is determined by several factors, including the design and size of the generator, the type of fuel used, and the intended use of the generator. It is important to follow the manufacturer's guidelines and specifications for the appropriate speed for your specific generator.

5. How can I control the speed of a generator rotor?

The speed of a generator rotor can be controlled by adjusting the throttle or using a governor. A governor is a mechanical device that monitors and regulates the speed of the rotor to maintain a constant output. In some generators, the speed can also be controlled by adjusting the amount of fuel being supplied to the engine.

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