In the question whay v(0)=0 v?! 4 The switch in Fig. 8.69 moves from position A to position B at t= 0 (please note that the switch must connect to point B before it breaks the connection at A, a make-before-break switch). Find v() for t> 0. 302 4 H B 20 V 0.25 F () 10 Figure 8.69
In the question whay v(0)=0 v?! 4 The switch in Fig. 8.69 moves from position A to position B at t= 0 (please note that the switch must connect to point B before it breaks the connection at A, a make-before-break switch). Find v() for t> 0. 302 4 H B 20 V 0.25 F () 10 Figure 8.69
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Transcribed Image Text:In the question whay
v(0)=0 v?!
8.14 The switch in Fig. 8.69 moves from position A to
position B at t = 0 (please note that the switch must
connect to point B before it breaks the connection at
A, a make-before-break switch). Find v(t) for t> 0.
30 2
4 H
ww
ele
B9
20 V
0.25 F (1)
102
Figure 8.69
For Prob. 8,14.
Chapter 8, Solution 14.
When the switch is in position A, v(0)=0 and i(0) =
20
= 0.5A. When the switch is in
40
position B, we have a source-free series RCL circuit.
R
10
=1.25
2x4
%3D
2L
1
3D1
%3D
VLC
x4
Since a > w,, we have overdamped case.
S12 = -a t Ja - w = -1.25t 1.5625-1= -0.5 and -2
v(t) = Ae 2+ Be0.5t
(1)
v(0) = 0 = A + B
(2)
i(0) = c
dv(0)
= 0.5
dt
dv(0) 0.5
dt
dv(t)
= -2Ae-2t -0.5Be-0.5t
dt
But
dv(0)
=-2A - 0.5B = 2
dt
(3)
Solving (2) and (3) gives A=-1.3333 and B = 1.3333
v(t) =-1.3333e 4 + 1.3333e 0.5t V.
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