High School

We appreciate your visit to Consider a generator that rotates its 200 turn 0 15 m diameter coil at 3700 rpm in a 0 95 T field How many volts. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Consider a generator that rotates its 200-turn, 0.15 m diameter coil at 3700 rpm in a 0.95 T field. How many volts are induced in the coil?

A) 45 V
B) 90 V
C) 120 V
D) 150 V

Answer :

Final answer:

The voltage induced in the coil can be calculated using Faraday's law of electromagnetic induction. By applying the formula for induced emf and converting the given parameters, the calculated induced peak voltage is approximately 120 V, making option C) 120 V the correct answer.

Explanation:

To calculate the voltage induced in the coil, we can use Faraday's law of electromagnetic induction which states that the induced electromotive force (emf) in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit. Since the coil is rotating in a magnetic field, the rate of change of flux is at its maximum when the coil is perpendicular to the field.

The formula for the induced emf (E) is E = NABw sin(wt), where:

  • N is the number of turns in the coil,
  • A is the area of the coil,
  • B is the magnetic field strength,
  • w is the angular velocity in radians per second, and
  • sin(wt) is the sine of the angular displacement which is 1 at the peak voltage.

The diameter of the coil is 0.15 m, so the radius (r) is 0.15 m / 2 = 0.075 m. Thus, the area (A) is πr2, or π(0.075 m)2.

To find the angular velocity (w), we convert the revolutions per minute (rpm) to radians per second. There are 2π radians in a revolution and 60 seconds in a minute:

w = rpm × (2π radians/revolution) × (1 minute/60 seconds)

w = 3700 × (2π / 60)

w ≈ 386.9 radians/second

Now we can calculate the peak voltage (E) induced in the coil:

E = NABw sin(wt)

E = 200 turns × π(0.075 m)2 × 0.95 T × 386.9 radians/second

E ≈ 120 volts

The induced voltage in the coil is approximately 120 V, so the correct answer is C) 120 V.

Thanks for taking the time to read Consider a generator that rotates its 200 turn 0 15 m diameter coil at 3700 rpm in a 0 95 T field How many volts. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada