Page 125 - Schaum's Outline of Theory and Problems of Electric Circuits

WAVEFORMS AND SIGNALS
114

Fig. 6-13 [CHAP. 6

EXAMPLE 6.23 The voltage v ¼ V 0 e jtj= , > 0, is connected to a capacitor. Find the current i in the capacitor.
Sketch v and i for V 0 ¼ 10 V, C ¼ 1 mF, and ¼ 1 ms.
Using i ¼ Cdv=dt,
for t < 0; v ¼ V 0 e t= and i ¼ I 0 e t=
for t > 0; v ¼ V 0 e t= and i ¼ I 0 e t=
where I 0 ¼ CV 0 = .
For V 0 ¼ 10 V, C ¼ 1 mF, and ¼ 10 3 s, we get I 0 ¼ 10 mA. Graphs of v and i are shown in Figs. 6-14(a) and
(b), respectively.

Fig. 6-14

6.11 DAMPED SINUSOIDS
A damped sinusoid, with its amplitude decaying exponentially has the form

vðtÞ¼ Ae at cos ð!t þ Þ ð38Þ

This function will be discussed in more detail in Chapter 8.

at
EXAMPLE 6.24 The current i ¼ I 0 e cos !t passes through a series RL circuit. (a) Find v RL , the voltage across
this combination. (b) Compute v RL for I 0 ¼ 3A, a ¼ 2, ! ¼ 40 rad/s, R ¼ 5
and L ¼ 0:1 H. Sketch i as a
function of time.