Basic Engineering Circuit Analysis
11th Edition
ISBN: 9781118992661
Author: Irwin, J. David, NELMS, R. M., 1939-
Publisher: Wiley,
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Textbook Question
Chapter 1, Problem 24P
Element B in the diagram in Fig. P1.24 supplies 60 W of power. Calculate
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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
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13
F
5 Ω it (t)
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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} =
A single-core cable working on 66 kV has a conductor diameter of 2 cm and the sheath of inside diameter
is 10 cm. If two metallic intersheaths of diameters 5 cm, 8 cm respectively are used for grading the cable.. If
the maximum electric stress is the same for each layers.
1- Find the voltage of each metallic intersheaths.
2- Find the thickness of each layers.
Chapter 1 Solutions
Basic Engineering Circuit Analysis
Ch. 1 - If the current in an electric conductor is 2.4 A,...Ch. 1 - Determine the time interval required for a 12�A...Ch. 1 - A lightning bolt carrying 30,000 A lasts for 50...Ch. 1 - If a 12-V battery delivers 100 J in 5 s, find (a)...Ch. 1 - The current in a conductor is 1.5 A. How many...Ch. 1 - If 60 C of charge pass through an electric...Ch. 1 - Determine the number of coulombs of charge...Ch. 1 - Five coulombs of charge pass through the element...Ch. 1 - The current that enters an element is shown in...Ch. 1 - The charge entering the positive terminal of an...
Ch. 1 - The charge entering the positive terminal of an...Ch. 1 - Prob. 12PCh. 1 - The power absorbed by the BOX in Fig. Pl. 13 is...Ch. 1 - The power absorbed by the BOX in Fig. Pl. 14 is...Ch. 1 - The energy absorbed by the BOX in Fig. P1.15 is...Ch. 1 - The charge that enters the BOX in Fig. P1.16 is...Ch. 1 - The energy absorbed by the BOX in Fig. Pl. 17 is...Ch. 1 - The charge entering the upper terminal of the BOX...Ch. 1 - The energy absorbed by the BOX in Fig. Pl. 19 is...Ch. 1 - Determine the amount of power absorbed or supplied...Ch. 1 - Calculate the power absorbed by element A in Fig....Ch. 1 - Calculate the power supplied by element A in Fig....Ch. 1 - Element A in the diagram in Fig. PI .23 absorbs 30...Ch. 1 - Element B in the diagram in Fig. P1.24 supplies 60...Ch. 1 - Element B in the diagram in Fig. PI .25 supplies...Ch. 1 - Element B in the diagram in Fig. Pl.26 supplies 72...Ch. 1 - (a) In Fig. Pl.27 (a), P1=36W. Is element 2...Ch. 1 - Two elements are connected in series, as shown in...Ch. 1 - Element 2 in Fig. Pl.29 absorbed 32W. Find the...Ch. 1 - Choose Is such that the power absorbed by element...Ch. 1 - Find the power that is absorbed or supplied by the...Ch. 1 - Find the power that is absorbed or supplied by the...Ch. 1 - Compute the power that is absorbed or supplied by...Ch. 1 - Find the power that is absorbed or supplied by...Ch. 1 - Find Ix in the network in Fig. P1.35.Ch. 1 - Prob. 36PCh. 1 - Find the power absorbed or supplied by element 1...Ch. 1 - Find the power absorbed or supplied by element 3...Ch. 1 - Find the power absorbed or supplied by element 1...Ch. 1 - Find Vx in the network in Fig. P1.40 using...Ch. 1 - Find Ix in the circuit in Fig. P1.41 using...Ch. 1 - Is the source Vs in the network in Fig. P1.42...Ch. 1 - Find I0 in the network in Fig. P1.43 using...Ch. 1 - Calculate the power absorbed by each element in...Ch. 1 - Calculate the power absorbed by each element in...Ch. 1 - In the circuit in Fig. P1.46, element 1 absorbs 40...
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