Question

a 280-loop circular armature coil with a diameter of 13.0 cm rotates at 120 rev/s in a uniform magnetic field of strength 0.45 t . part a what is the rms voltage output of the generator? express your answer with the appropriate units.

Answer 1

To find the RMS voltage output of a generator, the peak voltage must first be calculated using the number of turns, angular velocity, magnetic field strength, and area of the coil. The peak voltage is then divided by the square root of two to obtain the RMS voltage.

Step-by-step explanation:

Calculating RMS Voltage Output of a Generator

To calculate the RMS voltage output of a generator, we need to perform several steps involving the physical principles of electromagnetic induction.

The given information states that we have a 280-loop circular armature coil with a diameter of 13.0 cm, rotating at 120 revolutions per second in a uniform magnetic field with a strength of 0.45 T. First, we need to determine the peak voltage (or maximum emf) using Faraday's law of induction and then calculate the RMS voltage.

The peak emf is given by the equation:

• emf = N × Ω × B × A,

where N is the number of turns, Ω is the angular velocity, B is the magnetic field strength, and A is the area of the coil.

Let's convert the diameter to radius (r = diameter / 2) and the revolutions per second into radians per second (Ω = rev/s × 2π).

The area (A) of the circular coil is:

• A = π × r²,

Next, we use these values to calculate the peak voltage:

emf = 280 × (120 × 2π) × 0.45 T × (π × (0.065 m)²).

Then to find the RMS voltage (Vrms), we use the relation:

• Vrms = emf_peak / √2.

After calculating the peak emf using the formula, you divide by √2 to find the RMS voltage, which will be expressed in volts (V).

This methodology represents a typical application of electromagnetic theory in physics to predict the behavior of electric generators.