Schaum's Outline of Basic Circuit Analysis by John O'Malley

Author:John O'Malley
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2011-05-31T16:00:00+00:00

Fig. 10-8

The waveform shown in Fig. 10-8a is a sinusoid “riding” on top of a constant 3 V. Since the average value of the sinusoid is zero, the average value of the waveform equals the constant 3 V.

The average value of the waveform shown in Fig. 10-86, and of any waveform, is the area under the waveform for one period, divided by the period. Since for the cycle beginning at t = 0 s, the waveform is at 8 V for half a period and is at 1 V for the other half-period, the area underneath the curve for this one cycle is, from the height-times-base formula for a rectangular area, 8 × T/2 + 1 × T/2 = 4.5T. So, the average value is 4.5T/T=4.5V. Note that the average value does not depend on the period. This is generally true.

The cycle of the waveform shown in Fig. 10-8c beginning at f = 0 s is a triangle with a height of 10 and a base of T. The area under the curve for this one cycle is, from the triangular area formula of one-half the height times the base, 0.5 × 10 × T= 57. And so the average value is 5T/T= 5 V.

10.22 What are the average values of the periodic waveforms shown in Fig. 10-9?

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