Average Value

Chapter 6.4 Average Value

Fundamental Electrical and Electronic Principles Third Edition Book
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Fundamental Electrical and Electronic Principles Third Edition Book

  • Alternating Quantities 203 (b) 357520035752000 4667 sin() milliampsin()tt. therefore, sin * radso, 2000 46670 48550 4855200tt1...00 773.ms Ans t (s)0 Fig. 6.4 i1 i3IavImint (s) Fig. 6.5 6.4 Average Value Figure 6.4 shows one cycle of a sinusoidal current. A number of equally spaced intervals are selected, along the time axis of the graph. At each of these intervals, the instantaneous value is determined. *Remember , use RADIAN mode on your calculator. From this it is apparent that the area under the curve in the positive half is exactly the same as that for the negative half. Thus, the average value over one complete cycle must be zero. For this reason, the average value is taken to be the average over one half cycle. This average may be obtained in a number of ways. These include, the mid-ordinate rule, the trapezoidal rule, Simpson ’ s rule, and integral calculus. The simplest of these is the mid-ordinate rule, and this will be used here to illustrate average value; see Fig. 6.5 .