Electrical Engineering ⇒ Topic : Average Value of Sinusoidal Current

   The average value of alternating current (or voltage) over one cycle is zero. It is because the waveform is symmetrical about time axis and positive area exactly cancels the negative area. However, the average value over a half-cycle (positive or negative) is not zero. Therefore, average value of alternating current (or voltage) means half-cycle average value unless stated otherwise.

    The half-cycle average value of a.c. is that value of steady current (d.c) which would send the same amount of charge through a circuit for half the time period of a. c. as is sent by the a. c. through the same circuit in the same time. It is represented by I. This can be obtained by integrating the instantaneous value of current over one half cycle (i.e. area over half-cycle) and dividing the result by base length of half-cycle (= π).

The equation of an alternating current varying sinusoidally is given by

                                              i = I_m sin θ

Consider an elementary strip of thickness dθ in the first half-cycle of current wave as shown in Fig. (a).

Let i be the mid-ordinate of this strip.

                                                        figure (a)       

        Area of strip = i dθ

Clearly, average value of a.c. over a complete cycle is zero. Similarly, it can be proved that for alternating voltage varying sinusoidally , V_av = 0.637 V_m