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. The instantaneous value of the emf 30° is 51,84 pie. Determine the mathematical equation describing this wave. Express your answer in the form of e=Emax × sin (w×t)
To determine the mathematical equation describing the wave, we need to find the amplitude and angular frequency.
The amplitude, Eₘₐₓ, is the maximum value of the emf. Given that the instantaneous emf at 30° is 51.84π, we can use the equation for emf:
e = Eₘₐₓ × sin(ωt)
At 30°, sin(30°) = 0.5, so we can rewrite the equation as:
51.84π = Eₘₐₓ × 0.5
Eₘₐₓ = (51.84π) / 0.5
Eₘₐₓ = 103.68π
The angular frequency, ω, is given by:
ω = 2πf
Where f is the frequency, given as 40 Hz. Therefore,
ω = 2π × 40
ω = 80π
So, the mathematical equation describing the wave is:
e = 103.68π × sin(80πt)