Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
9th Edition
ISBN: 9781259989452
Author: Hayt
Publisher: Mcgraw Hill Publishers
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Textbook Question
Chapter 8.6, Problem 10P
For the circuit of Fig. 8.37, find vc(t) at t equal to (a) 0−; (b) 0+; (c) ∞; (d) 0.08 s.
■ FIGURE 8.37
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2.
Consider the following electrical system:
R
L
C= Uc
The equations describing the system dynamics are the following:
di(t)
u(t) = Lº
+(R, +R, )i(t)+u̟(t)
dt
c du (t)
= i(t)
dt
Choose as state variables: x, (t) = u.(t) and x, (t) = i(t).
Obtain the following state space model
1
-
C
+ 1 u
R, + R, |X2
L
1
L
y =[1 0]
+ Ou
and calculate the system matrices for L = 0.5, R1 = 1, R2 = 1and C = 1.
From the state space model obtain the transfer function of the system.
By using controllability gramian, check if the system representation R(A,B,C) is
controllable.
Design a state feedback u(t) = -Kx(t), which will place the closed-loop poles on
desired locations: 14 = -1 and 14 = -2.
By using observability matrix, check if the system representation R(A, B,C) is
observable.
Design a reduced-order state observer with desired poles 2d = -2.
With reference to the simple circuit of figure 8, compute i(t) for
(a) t = 0- ; (b) t = 0*; (c) t = 1"; (d) t = 1*; (e) t = 2ms
1H
all
i(t)
Figure 8 9u(t – 1) v
3 kN
8.4 Step-Response Series
RLC Circuits (3)
Example 4
Having been in position for a long time, the
switch in the circuit below is moved to position b
at t = 0. Find v(t) and vR(t) for t > 0.
2.5 H
10Ω
a
ww-
12 V
22
10 V
• Please refer to lecture or textbook for more detail elaboration.
Answer: v(t) = {10 + [(-2cos3.464t – 1.1547sin3.464t)e-2t]} V
VR(t)= [2.31sin3.464t]e-2t V
15
-19
ww
Chapter 8 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
Ch. 8.1 - For the circuit in Fig. 8.2, what value of...Ch. 8.1 - Noting carefully how the circuit changes once the...Ch. 8.2 - In a source-free series RC circuit, find the...Ch. 8.3 - Prob. 4PCh. 8.3 - Prob. 5PCh. 8.4 - Prob. 6PCh. 8.4 - Prob. 7PCh. 8.4 - Prob. 8PCh. 8.5 - Evaluate each of the following at t = 0.8: (a)...Ch. 8.6 - For the circuit of Fig. 8.37, find vc(t) at t...
Ch. 8.7 - Prob. 11PCh. 8.7 - The voltage source 60 40u(t) V is in series with...Ch. 8.7 - Prob. 13PCh. 8.8 - Prob. 14PCh. 8.8 - Prob. 15PCh. 8 - A source-free RC circuit has R = 4 k and C = 22 F,...Ch. 8 - A source-free RC circuit has v(0) = 12 V and R =...Ch. 8 - The resistor in the circuit of Fig. 8.51 has been...Ch. 8 - Prob. 4ECh. 8 - Prob. 5ECh. 8 - Prob. 6ECh. 8 - Prob. 7ECh. 8 - Prob. 8ECh. 8 - Prob. 9ECh. 8 - The switch in Fig. 8.56 has been closed for a long...Ch. 8 - For the circuit in Fig. 8.56, find (a) the total...Ch. 8 - Design a capacitor-based circuit that can achieve...Ch. 8 - (a) Graph the function f (t) = 10e2t over the...Ch. 8 - The current i(t) flowing through a 1 k resistor is...Ch. 8 - Radiocarbon dating has a similar exponential time...Ch. 8 - For the circuit of Fig. 8.4, compute the time...Ch. 8 - Design a circuit which will produce a current of 1...Ch. 8 - Prob. 18ECh. 8 - Prob. 19ECh. 8 - Referring to the circuit shown in Fig. 8.11,...Ch. 8 - Prob. 21ECh. 8 - With the assumption that the switch in the circuit...Ch. 8 - The switch in Fig. 8.57 has been closed since...Ch. 8 - The switch in the circuit of Fig. 8.58 has been...Ch. 8 - Assuming the switch initially has been open for a...Ch. 8 - (a) Obtain an expression for v(t), the voltage...Ch. 8 - For the circuit of Fig. 8.61, determine ix, iL,...Ch. 8 - Prob. 28ECh. 8 - Prob. 29ECh. 8 - Prob. 30ECh. 8 - Prob. 31ECh. 8 - (a) Obtain an expression for vx as labeled in the...Ch. 8 - Prob. 33ECh. 8 - Prob. 34ECh. 8 - Prob. 35ECh. 8 - Prob. 36ECh. 8 - Prob. 37ECh. 8 - The switch in Fig. 8.70 is moved from A to B at t...Ch. 8 - Prob. 39ECh. 8 - Prob. 40ECh. 8 - Evaluate the following functions at t = 1, 0, and...Ch. 8 - Prob. 42ECh. 8 - Prob. 43ECh. 8 - Prob. 44ECh. 8 - You can use MATLAB to represent the unit-step...Ch. 8 - With reference to the circuit depicted in Fig....Ch. 8 - For the circuit given in Fig. 8.75, (a) determine...Ch. 8 - Prob. 48ECh. 8 - Prob. 49ECh. 8 - You build a portable solar charging circuit...Ch. 8 - The switch in the circuit of Fig. 8.78 has been...Ch. 8 - The switch in the circuit of Fig. 8.78 has been...Ch. 8 - Prob. 53ECh. 8 - Prob. 54ECh. 8 - Prob. 55ECh. 8 - For the circuit represented in Fig. 8.82, (a)...Ch. 8 - Prob. 58ECh. 8 - Prob. 59ECh. 8 - For the circuit given in Fig. 8.85, (a) determine...Ch. 8 - The circuit depicted in Fig. 8.86 contains two...Ch. 8 - Prob. 62ECh. 8 - Prob. 63ECh. 8 - A series RL circuit has a voltage that steps from...Ch. 8 - For the two-source circuit of Fig. 8.89, note that...Ch. 8 - (a) Obtain an expression for iL as labeled in Fig....Ch. 8 - Obtain an expression for i(t) as labeled in the...Ch. 8 - Obtain an expression for i1 as indicated in Fig....Ch. 8 - Plot the current i(t) in Fig. 8.93 if (a) R = 10 ;...Ch. 8 - A dc motor can be modeled as a series RL circuit...Ch. 8 - Prob. 71ECh. 8 - Prob. 72ECh. 8 - A series RC sequentially switched circuit has R =...Ch. 8 - Refer to the circuit of Fig. 8.95, which contains...Ch. 8 - In the circuit of Fig. 8.95, a 3 mF capacitor is...Ch. 8 - Prob. 78E
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- 2. Consider the following electrical system: R, Uc u RI he equations describing the system dynamics are the following: di(t) +(R +R,)i(t)+u (t) dt u(t) = L- du (t) C- = i(t) dt Choose as state variables: x, (t) = u̟(t) and x,(t) = i(t). Obtain the following state space model 1 X1 + 1 u C R + R, |LX2 L 1 -- L L y=[1 0] + Ou X2 and calculate the system matrices for L = 0.5, R1 = 1, R2 = 1and C = 1. From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A, B,C) is controllable.arrow_forwardThe switch in Fig. 8.73 is moved from A to B at t = 0 after being at A for along time. This places the two capacitors in series, thus allowing equal andopposite dc voltages to be trapped on the capacitors. (a) Determine v1(0−),v2(0−), and vR(0−). (b) Find v1(0+), v2(0+), and vR(0+). (c) Determine thetime constant of vR(t). (d) Find vR(t), t > 0. (e) Find i(t). ( f ) Find v1(t) andv2(t) from i(t) and the initial values. (g) Show that the stored energy at t = ∞plus the total energy dissipated in the 20 k-resistor is equal to the energystored in the capacitors at t = 0.arrow_forward2. Consider the following electrical system: R Uc C = i The equations describing the system dynamics are the following: di(t) +(R, + R, )i(t)+u (t) dt u(t) = L- c du (t) C- = i(t) dt Choose as state variables: x, (t) =u¸(t) and x, (t) = i(t). %D Obtain the following state space model 1 + 1 u 1 R + R, Lx2 L y = [1 0] + Ou X2 and calculate the system matrices for L = 1, R1 = 1, R2 = 1and C = 0.5. From the state space model obtain the transfer function of the system. By using controllability gramian, check if the system representation R(A,B,C) is controllable. ||arrow_forward
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