Schaum,s Outlines Basic Circuit Analysis, Second Edition by John O’Malley Ph.D

Author:John O’Malley, Ph.D.
Language: eng
Format: epub
Publisher: McGraw-Hill
Published: 2011-07-14T16:00:00+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?

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.