Question

Calculate the average value of the sinusoidal waveform y(t)=4.56cos(77.64πt+4800π÷68).

(a) 41 V

(b) 0 V

(c) 48 V

(d) 78 V

I had been asked this question in semester exam.

Origin of the question is Induction Motors topic in division Speed Control of Direct Current Motors & Induction Motors of Electric Drives

Answer 1

Correct choice is (b) 0 V

To elaborate: Sinusoidal waveform is generally expressed in the form of V=Vmsin(ωt+α) where Vm represents peak value, ω represents angular frequency, α represents a phase difference. The average value of a sine wave is zero because of equal and opposite lobes areas. Since sine wave is an odd function then the net area of the waveform over a period is Net area = A+(-A) = 0. The average value is Net area÷Time=0.