Question

A 600-loop circular armature coil with a diameter of 9.0 cm rotates at 190 rev/s in a uniform magnetic field of strength 0.55 T .

What is the rms voltage output of the generator?

Express your answer to two significant figures and include the appropriate units.

Answer 1

Comment for any further help.

Answer 2

To calculate the rms voltage output of the generator, we can use Faraday's law of electromagnetic induction, which states that the induced voltage (V) in a coil is equal to the rate of change of magnetic flux (Φ) through the coil.

The magnetic flux through a coil is given by the equation:

Φ = B * A * cos(θ)

where B is the magnetic field strength, A is the area of the coil, and θ is the angle between the magnetic field and the normal to the coil's surface.

In this case, the coil is circular, so its area (A) can be calculated using the formula:

A = π * r^2

where r is the radius of the coil.

Given: Number of loops (N) = 600 Diameter of the coil = 9.0 cm Radius (r) = diameter / 2 = 9.0 cm / 2 = 4.5 cm = 0.045 m Rotation frequency (f) = 190 rev/s Magnetic field strength (B) = 0.55 T

First, let's calculate the area of the coil:

A = π * r^2 = π * (0.045 m)^2

Next, let's calculate the rate of change of magnetic flux (dΦ/dt) by multiplying the magnetic field strength (B) by the change in the magnetic flux, which is the product of the area (A) and the rotation frequency (f):

dΦ/dt = B * A * f

Finally, the rms voltage output (V) can be calculated by multiplying the rate of change of magnetic flux (dΦ/dt) by the number of loops (N):

V = N * dΦ/dt

Let's plug in the values and calculate the rms voltage output:

A = π * (0.045 m)^2 dΦ/dt = B * A * f V = N * dΦ/dt

A = π * (0.045 m)^2 dΦ/dt = (0.55 T) * A * (190 rev/s) V = (600) * dΦ/dt

Calculating A:

A = π * (0.045 m)^2 ≈ 0.0063617 m^2

Calculating dΦ/dt:

dΦ/dt = (0.55 T) * (0.0063617 m^2) * (190 rev/s) ≈ 0.038599 V·s

Calculating V:

V = (600) * (0.038599 V·s) ≈ 23.16 V

Therefore, the rms voltage output of the generator is approximately 23.16 V.