EBK ELECTRIC CIRCUITS
10th Edition
ISBN: 8220100801792
Author: Riedel
Publisher: YUZU
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Question
Chapter 7, Problem 29P
a)
To determine
Calculate the value of
b)
To determine
Calculate the value of
c)
To determine
Calculate the value of
d)
To determine
Calculate the value of initial energy stored in the capacitor.
e)
To determine
Calculate the time taken by the circuit to dissipate 68 % of the initial energy stored in the capacitor.
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Introduction
The circuit of Fig. 1 is required to be modeled using a state - space representation, where 2
states will be used, based on the number of the energy - storing elements of the circuit, the
capacitor and the inductor.
u(t)
+
ΙΩ
www
13
F
5 Ω it (t)
www
vc(t) 1 H
Figure 1: LCR circuit
The input signal to the circuit is the voltage u(t) in Volts and the output signal is the voltage
across the capacitor, vc(t).
Questions
1. Choice of system states:
Choose appropriate signals for the 2 states of the
system.
x₁(t) = i₁(t)
x₂ (t) =
5. State transition matrix:
(t), which is defined as,
Calculate analytically the state transition matrix
(t) = et = L¯¹{(sI – A)¯¹}
Show that the answer is the following,
1
e-4t cos(√2t) -
e-4 sin(√2 t)
1
e
-4t
√2
(t) = et
-3
1
-4t sin (√2 t)
e
COS
-4t cos (√2t) + -
e
sin(√2 t)
2-4t sin(√2 t)|
Calculate the following:
(SI - A)-1=
Use the completion - in - the-square technique (CASE 3) to calculate the inverse Laplace:
L¯¹{(SI - A)¯¹} =
Chapter 7 Solutions
EBK ELECTRIC CIRCUITS
Ch. 7.1 - The switch in the circuit shown has been closed...Ch. 7.1 - Prob. 2APCh. 7.2 - Prob. 3APCh. 7.2 - Prob. 4APCh. 7.3 - Prob. 5APCh. 7.3 - Prob. 6APCh. 7.5 - Prob. 7APCh. 7.5 - Prob. 8APCh. 7.7 - There is no energy stored in the capacitor at the...Ch. 7.7 - Prob. 10AP
Ch. 7 - Prob. 1PCh. 7 - Prob. 2PCh. 7 - In the circuit shown in Fig. P 7.2, the switch...Ch. 7 - Prob. 4PCh. 7 - Prob. 5PCh. 7 - The two switches in the circuit seen in Fig. P...Ch. 7 - Prob. 7PCh. 7 - Prob. 8PCh. 7 - The switch shown in Fig. P 7.4 has been open for a...Ch. 7 - Prob. 10PCh. 7 - In the circuit in Fig. P 7.11, let Ig represent...Ch. 7 - Prob. 12PCh. 7 - Prob. 13PCh. 7 - Prob. 14PCh. 7 - Prob. 15PCh. 7 - Prob. 16PCh. 7 - Prob. 17PCh. 7 - For the circuit seen in Fig. P 7.19, find
the...Ch. 7 - Prob. 19PCh. 7 - Prob. 20PCh. 7 - Prob. 21PCh. 7 - Prob. 22PCh. 7 - Prob. 23PCh. 7 - Prob. 24PCh. 7 - Prob. 25PCh. 7 - In the circuit shown in Fig. P 7.26, both switches...Ch. 7 - The switch in the circuit in Fig. P 7.25 is closed...Ch. 7 - Prob. 28PCh. 7 - Prob. 29PCh. 7 - Prob. 30PCh. 7 - The switch in the circuit seen in Fig. P 7.30 has...Ch. 7 - In Problem 7.30 how many microjoules of energy are...Ch. 7 - Prob. 33PCh. 7 - Prob. 35PCh. 7 - The switch in the circuit shown in Fig. P 7.38 has...Ch. 7 - Prob. 37PCh. 7 - Prob. 38PCh. 7 - Prob. 39PCh. 7 - Prob. 40PCh. 7 - Prob. 41PCh. 7 - Prob. 42PCh. 7 - Prob. 43PCh. 7 - Prob. 44PCh. 7 - Prob. 45PCh. 7 - Prob. 46PCh. 7 - Prob. 47PCh. 7 - For the circuit in Fig. P 7.4, find (in...Ch. 7 - Prob. 49PCh. 7 - Prob. 50PCh. 7 - Prob. 51PCh. 7 - Prob. 52PCh. 7 - The switch in the circuit of Fig. P 7.55 has been...Ch. 7 - Prob. 54PCh. 7 - The switch in the circuit seen in Fig. P 7.56 has...Ch. 7 - Prob. 56PCh. 7 - Prob. 57PCh. 7 - Prob. 58PCh. 7 - Prob. 59PCh. 7 - Prob. 60PCh. 7 - Prob. 61PCh. 7 - Prob. 62PCh. 7 - Prob. 64PCh. 7 - Prob. 65PCh. 7 - Prob. 66PCh. 7 - Prob. 67PCh. 7 - Prob. 68PCh. 7 - Prob. 69PCh. 7 - Prob. 70PCh. 7 - Prob. 71PCh. 7 - Prob. 72PCh. 7 - For the circuit in Fig. P 7.73, how many...Ch. 7 - Prob. 74PCh. 7 - Prob. 75PCh. 7 - Prob. 76PCh. 7 - Prob. 77PCh. 7 - Prob. 78PCh. 7 - Prob. 79PCh. 7 - Prob. 80PCh. 7 - Prob. 81PCh. 7 - Prob. 82PCh. 7 - Prob. 84PCh. 7 - Prob. 85PCh. 7 - Prob. 86PCh. 7 - Prob. 87PCh. 7 - Prob. 88PCh. 7 - Prob. 90PCh. 7 - Prob. 91PCh. 7 - Prob. 92PCh. 7 - Prob. 93PCh. 7 - Prob. 94PCh. 7 - Prob. 95PCh. 7 - Prob. 102PCh. 7 - Prob. 103PCh. 7 - Prob. 104PCh. 7 - Prob. 105PCh. 7 - Prob. 106PCh. 7 - Prob. 107P
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