A four-pole alternator has a uniform magnetic flux density of 0,5 T. A square coil with 200 turns and sides of 18cm is rotated at 20 r/s inside the field. The frequency is equal to 40 Hz and time period is 0,025 s. Determine instantaneous value of the emf 30° after reaching maximum.
To find the instantaneous value of the emf 30° after reaching the maximum, we will use the equation for the emf induced in a rotating coil:
Emf = N * B * A * ω * sin(θ)
Where:
N = number of turns of the coil (200 turns)
B = magnetic flux density (0.5 T)
A = area of the coil (side length of the square coil)^2 = (0.18 m)^2 = 0.0324 m^2
ω = angular velocity (20 r/s * 2π rad/r)
θ = angle between the normal to the plane of the coil and the magnetic field direction (30°)
First, let's calculate the angular velocity ω:
ω = 20 r/s * 2π rad/r = 40π rad/s
Now, we can substitute the values into the equation:
Emf = 200 * 0.5 T * 0.0324 m^2 * 40π rad/s * sin(30°)
Emf = 200 * 0.5 * 0.0324 * 40π * sin(30°)
Emf ≈ 103.68π * sin(30°)
Using sin(30°) = 0.5, we can simplify further:
Emf ≈ 103.68π * 0.5
Emf ≈ 51.84π
Therefore, the instantaneous value of the emf 30° after reaching the maximum is approximately 51.84π volts.