Page 202 - Schaum's Outline of Theory and Problems of Electric Circuits
P. 202
Sinusoidal Steady-
State Circuit Analysis
9.1 INTRODUCTION
This chapter will concentrate on the steady-state response of circuits driven by sinusoidal sources.
The response will also be sinusoidal. For a linear circuit, the assumption of a sinusoidal source
represents no real restriction, since a source that can be described by a periodic function can be replaced
by an equivalent combination (Fourier series) of sinusoids. This matter will be treated in Chapter 17.
9.2 ELEMENT RESPONSES
The voltage-current relationships for the single elements R, L,and C were examined in Chapter 2
and summarized in Table 2-1. In this chapter, the functions of v and i will be sines or cosines with the
argument !t. ! is the angular frequency and has the unit rad/s. Also, ! ¼ 2 f , where f is the frequency
with unit cycle/s, or more commonly hertz (Hz).
Consider an inductance L with i ¼ I cos ð!t þ 458Þ A [see Fig. 9-1(a)]. The voltage is
di
v L ¼ L ¼ !LI½ sin ð!t þ 458Þ ¼ !LI cos ð!t þ 1358Þ ðVÞ
dt
Fig. 9-1
191
Copyright 2003, 1997, 1986, 1965 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
