A voltmeter and frequency meter connected across the supply of a circuit give :220 v and 50 Hz .determine the mathematical equation and form factor
The equation for voltage can be written as:
V(t) = Vm * sin(2πft)
where:
V(t) is the instantaneous voltage at time t,
Vm is the maximum voltage (in this case, 220 V),
f is the frequency (in this case, 50 Hz),
and t is the time.
The form factor can be calculated by dividing the root mean square (RMS) voltage by the average voltage. In this case, the RMS voltage is 220 V, and the average voltage can be found by integrating the equation over one complete cycle (0 to T):
Average voltage (Vav) = (1/T) * ∫[0 to T] V(t) dt
Since the voltage is sinusoidal, the integral simplifies to:
Vav = (2/T) * ∫[0 to T/4] Vm * sin(2πft) dt
Using trigonometric identities, we have:
Vav = (2/T) * [- (Vm/2πf) * cos(2πft)] [0 to T/4]
At t = T/4, cos(2πft) becomes zero, so we have:
Vav = (2/T) * (- (Vm/2πf) * cos(2πf(T/4)))
Since cos(π/2) = 0, the above equation simplifies to:
Vav = 0
Therefore, the average voltage is 0.
Now we can calculate the form factor:
Form factor = RMS voltage / Average voltage
= RMS voltage / 0
= infinity
So the form factor in this case is infinity.