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, Problem 46E
With reference to the circuit depicted in Fig. 8.74, compute v(t) for (a) t = 0−; (b) t = 0+; (c) t = 2 ms; (d) t = 5 ms.
FIGURE 8.74
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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
The 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.
Figure 8 showsa resistor inductor capacitor (RLC) circuit. The input to the system is
the voltage v(t) and the output of the circuit is the current iz (t).
8
R,
i(t)
iz(t)
v(t)
Ve(t)
R2
Figure 8
a)
Determine differential equations containing i, (t), iz (t) and v. (t) for the
appropriate meshes and nodes.
b) Assuming zero initial conditions
i)
derive Laplace transformations of the differential equations found in a)
ii)
determine the transfer function G(s) =
I2(s)
VIs where l2(s) = L{i2 (t}}
and V(s) = L{v(t}.
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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