Electromagnetic Induction of ac generator

In summary, the coil of an ac generator with an area per turn of 1.2x10-2m2 and 500 turns in a 0.13-T magnetic field rotating at 34 rads/s has an emf induced of 12.03V when the normal to the loop makes an angle of 27 degrees with respect to the direction of the magnetic field. This is determined by using the equation E=NABw(sin(wt)). The previous attempt at a solution resulted in 75V, which was likely due to confusion between frequency and angular speed.
  • #1
sadean1s
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Homework Statement


The coil of an ac generator has an area per turn of 1.2x10-2m2 and consists of 500 turns. The coil is situated in a 0.13-T magnetic field and is rotating at an angular speed of 34 rads/s. What is the emf induced in the coil at the instant when the normal to the loop makes an angle of 27 degrees with respect to the direction of the magnetic field?


Homework Equations


E=NAB[tex]\varpi[/tex]sin[tex]\varpi[/tex]t

The Attempt at a Solution


after plugging in the numbers into the equation I got 75 V. The answer is 12V
 
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  • #2
So you're on the right track you do use the equation E=NABw(sin(wt)) but I don't know how you got 75V. Its a simple plug and chug: E= (500)(1.2x10^-2)(0.13)(34)(sin (27))= 12.03V
 
  • #3
The ratio of 75 to 12 is 6.25, very close to 2*pi. Perhaps the error stems from confusing f with omega?
 

1. What is electromagnetic induction?

Electromagnetic induction is the process by which a changing magnetic field can induce a current in a conductor, creating an electrical voltage. This was first discovered by Michael Faraday in the 1830s.

2. How does an AC generator work?

An AC generator uses electromagnetic induction to convert mechanical energy into electrical energy. As the rotor, which contains a permanent magnet, rotates within the stator, which contains a series of copper coils, the changing magnetic field induces a current in the coils, producing alternating current (AC) electricity.

3. What is the difference between AC and DC generators?

The main difference between AC (alternating current) and DC (direct current) generators is the type of current they produce. AC generators use electromagnetic induction to produce alternating current, while DC generators use a commutator to produce direct current.

4. How is the voltage of an AC generator controlled?

The voltage of an AC generator can be controlled by adjusting the speed of the rotor or by changing the number of turns in the stator coils. Higher speeds or more turns will result in a higher voltage output.

5. What are some real-world applications of AC generators?

AC generators are used in many different applications, including power plants, wind turbines, hydroelectric dams, and even in cars as part of the alternator. They are also used in small portable generators for backup power and in electronic devices to convert AC power to DC power.

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