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 determine the instantaneous value of the emf 30° after reaching its maximum, we can use the formula for the emf induced in a rotating coil:
Emf = N * B * A * ω * sin(θ)
Where:
Emf is the induced emf
N is the number of turns in the coil (200 turns)
B is the magnetic flux density (0.5 T)
A is the area of the coil (side of the square coil squared, A = 0.18 m * 0.18 m = 0.0324 m^2)
ω is the angular velocity (2πf, where f is the frequency in Hz)
θ is the angle between the plane of the coil and the magnetic field (30° in this case)
Substituting the given values into the formula:
Emf = 200 * 0.5 T * 0.0324 m^2 * 2π * 40 Hz * sin(30°)
Calculating:
Emf = 200 * 0.5 T * 0.0324 m^2 * 2π * 40 Hz * 0.5
Emf ≈ 32.83 V
Therefore, the instantaneous value of the emf 30° after reaching its maximum is approximately 32.83 V.