A voltmeter and frequency meter are connected across the supply of a circuit give the following readings: 220V and 50Hz. Determine:
a) The mathematical equation representing this voltage
b) the time it takes this voltage to reach 200v during the first half cycle of rotation
c) the form factor of this waveform
a) The mathematical equation representing this voltage can be represented as:
v(t) = 220*sin(2π*50t)
Where v(t) is the instantaneous voltage at time t.
b) In one complete cycle of rotation, there are 50 half cycles. Therefore, the time it takes for the voltage to reach 200V during the first half cycle of rotation can be calculated as:
Time = (1/2)*(1/50) = 0.01 seconds
c) The form factor can be calculated using the formula:
Form Factor = RMS value/ Average value
The RMS value of the voltage can be calculated as:
Vrms = (1/√2)*Vmax = (1/√2)*220 = 155.56V
The average value of the voltage can be calculated as:
Average value = (2/π)*Vrms = (2/π)*155.56 = 99.02V
Therefore, the form factor can be calculated as:
Form Factor = Vrms/ Average value = 155.56/99.02 ≈ 1.57