A voltmeter and frequency meter are connected across the terminals of a single alternator running on no load gave the reading of 777.7v and 50Hz determine the mathematical equation describing this open circuit?
the average value of the emf?
the time needed for the emf to reach 975v during the first half cycle of rotation
the magnitude of the emf during 45° after the beginning of the cycle
To find the mathematical equation describing the open circuit waveform, we can use the equation for a sinusoidal waveform:
V = Vm*sin(ωt + φ)
Where:
- V is the instantaneous voltage at a given time t,
- Vm is the peak voltage or amplitude,
- ω is the angular frequency (2πf),
- t is time, and
- φ is the phase angle.
From the provided information, we know that the peak voltage is 777.7V and the frequency is 50Hz. Therefore, we can write the equation as:
V = 777.7*sin(2π*50*t + φ)
Next, we can find the average value of the EMF by integrating the equation over a full cycle and dividing by the period. The average value of a sinusoidal waveform is zero, so the average value of the EMF would be:
Average EMF = 0V
To find the time needed for the EMF to reach 975V during the first half cycle of rotation, we need to find the time when the voltage equals 975V. Setting V = 975V in the equation, we have:
975 = 777.7*sin(2π*50*t + φ)
We don't have enough information to find the exact value of t without knowing the phase angle φ. However, we can approximate it using numerical methods.
To find the magnitude of the EMF during 45° after the beginning of the cycle, we need to convert the given angle in degrees to radians. Since one full cycle is 360°, 45° is equal to (45/360) * 2π radians. Therefore, the equation becomes:
EMF = 777.7*sin(2π*50*t + φ)
where t = (45/360)*(1/50) seconds.
Note: The exact values for the time and magnitude of the EMF during 45° after the beginning of the cycle can be found once the phase angle φ is known.