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 5, Problem 90P
Use source transformation to find
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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 5 Solutions
Basic Engineering Circuit Analysis
Ch. 5 - Find Io in the network in Fig. P5.1 using...Ch. 5 - Find Io in the network in Fig. P5.2 using...Ch. 5 - Find Io in the network in Fig. P5.3 using...Ch. 5 - Find Vo in the network in Fig. P5.4 using...Ch. 5 - Find Io in the circuit in Fig. P5.5 using...Ch. 5 - Find Io in the network in Fig. P5.6 using...Ch. 5 - Find Io in the circuit in Fig. P5.7 using...Ch. 5 - Find Vo in the network in Fig. P5.8 using...Ch. 5 - Find Vo in the network in Fig. P5.9 using...Ch. 5 - In the network in Fig. P5.l0, find using...
Ch. 5 - Find Io in the network in Fig. P5.11 using...Ch. 5 - Find Io in the network in Fig. P5.12 using...Ch. 5 - Find IA in the network in Fig. P5.13 using...Ch. 5 - Using superposition, find IA in the circuit in...Ch. 5 - Find IA in the network in Fig. P5.15 using...Ch. 5 - Using superposition, find Vo in the network in...Ch. 5 - Use superposition to find Io in the circuit in...Ch. 5 - Use superposition to find Io in the network in...Ch. 5 - Use superposition to find Vo in the circuit in...Ch. 5 - Find Vo in the circuit in Fig. P5.20 using...Ch. 5 - Find Io in the circuit in Fig. P5.21 using...Ch. 5 - Use superposition to find Io in the circuit in...Ch. 5 - Use superposition to find Io in the network in...Ch. 5 - Use superposition to find Io in the circuit in...Ch. 5 - Use Thévenins theorem to find Vo in the network...Ch. 5 - Use Thévenins theorem to find in the network in...Ch. 5 - Use Thévenins theorem to find Vo in the network...Ch. 5 - Find Io in the network in Fig. P5.28 using...Ch. 5 - Find Vo in the network in Fig. P5.28 using...Ch. 5 - Use Thévenins theorem to find 10 in the network...Ch. 5 - Find Vo in the network in Fig. P5.31 using...Ch. 5 - Find Io in the circuit in Fig. P5.32 using...Ch. 5 - Find Io in the network in Fig. P5.33 using...Ch. 5 - Find Io in the network in Fig. P5.34 using...Ch. 5 - Find Io in the circuit in Fig. P5.35 using...Ch. 5 - Find Io in the network in Fig. P5.36 using...Ch. 5 - Using Thévenins theorem, find IA in the circuit...Ch. 5 - Find Vo in the network in Fig. P5.38 using...Ch. 5 - Find Vo in the circuit in Fig. P5.39 using...Ch. 5 - Find Io in the circuit in Fig. P5.40 using...Ch. 5 - Find Vo in the network in Fig. P5.41 using...Ch. 5 - Find Io in the network in Fig. P5.42 using...Ch. 5 - Find Vo in Fig. P5.43 using Thévenins theorem.Ch. 5 - Use Thévenins theorem to find Vo in the circuit...Ch. 5 - Use Thévenins theorem to find Io in Fig. P5.45.Ch. 5 - Find Vo in the network in Fig. P5.46 using...Ch. 5 - Use Thévenins theorem to find Io in the network...Ch. 5 - Use Thévenins theorem to find Io in the circuit...Ch. 5 - Given the linear circuit in Fig. P5.49, it is...Ch. 5 - If an 8-k load is connected to the terminals of...Ch. 5 - Use Nortons theorem to find Io in the circuit in...Ch. 5 - Find Io in the network in Fig. P5.52 using Nortons...Ch. 5 - Use Nortons theorem to find Io in the circuit in...Ch. 5 - Use Nortons theorem to find Vo in the network in...Ch. 5 - Find Io in the network in Fig. P5.55 using Nortons...Ch. 5 - Use Nortons theorem to find Vo in the network in...Ch. 5 - Find Vo in the network in Fig. P5.57 using Nortons...Ch. 5 - Use Nortons theorem to find Io in the circuit in...Ch. 5 - Find Vo in the circuit in Fig. P5.59 using Nortons...Ch. 5 - Use Nortons theorem to find Io in the network in...Ch. 5 - Use Nortons theorem to find Io in the circuit in...Ch. 5 - In the network in Fig. P5.62, find Vo using...Ch. 5 - Use Thévenins theorem to find 10 in the circuit...Ch. 5 - Find Vo in the network in Fig. P5.64 using...Ch. 5 - Use Thévenins theorem to find Vo in the circuit...Ch. 5 - Find Io in the circuit in Fig. P5.66 using...Ch. 5 - Use Thévenins theorem to find Io in the circuit...Ch. 5 - Use Thévenins theorem to find Vo in the circuit...Ch. 5 - Find Vo in the network in Fig. P5.69 using...Ch. 5 - Use Nortons theorem to find Vo in the network in...Ch. 5 - Find Vo in the circuit in Fig. P5.71 using...Ch. 5 - Find Vo in the network in Fig. P5.72 using...Ch. 5 - Find Vo in the network in Fig. P5.73 using Nortons...Ch. 5 - Use Thévenins theorem to find the power supplied...Ch. 5 - Find Vo in the circuit in Fig. P5.75 using...Ch. 5 - Find Vo in the network in Fig. P5.76 using...Ch. 5 - Find Vo in the network in Fig. P5.77 using...Ch. 5 - Use Thévenins theorem to find I2 in the circuit...Ch. 5 - Use Thévenins theorem to find Vo in the circuit...Ch. 5 - Use Thévenins theorem to find Vo in the circuit...Ch. 5 - Use Thévenins theorem to find Io in the network...Ch. 5 - Use Thévenins theorem to find Vo in the network...Ch. 5 - Find the Thévenin equivalent of the network in...Ch. 5 - Find the Thévenin equivalent of the network in...Ch. 5 - Find the Thévenin equivalent of the circuit in...Ch. 5 - Find the Thévenin equivalent of the network in...Ch. 5 - Find the Thévenin equivalent circuit of the...Ch. 5 - Find Vo in the network in Fig. P5.88 using source...Ch. 5 - Find Io in the network in Fig. P5.89 using source...Ch. 5 - Use source transformation to find Vo in the...Ch. 5 - Find 10 in the network in Fig. P5.91 using source...Ch. 5 - Find Vo in the network in Fig. P5.92 using source...Ch. 5 - Use source transformation to find Io in the...Ch. 5 - Find the Thévenin equivalent circuit of the...Ch. 5 - Find Io in the circuit in Fig. P5.95 using source...Ch. 5 - Find Io in the network in Fig. P5.96 using source...Ch. 5 - Find Io in the network in Fig. P5.97 using source...Ch. 5 - Find Vo in the network in Fig. P5.98 using source...Ch. 5 - Find Io in the network in Fig. P5.99 using source...Ch. 5 - Find in the circuit in Fig. P5.100 using source...Ch. 5 - Use source transformation to find Io in the...Ch. 5 - Using source transformation, find Vo in the...Ch. 5 - Use source transformation to find Io in the...Ch. 5 - Use source transformation to find Io in the...Ch. 5 - Use source transformation to find 10 in the...Ch. 5 - Using source transformation, find 10 in the...Ch. 5 - Use source exchange to find Io in the network in...Ch. 5 - Use a combination of Y- transformation and source...Ch. 5 - Use source exchange to find Io in the circuit in...Ch. 5 - Use source exchange to find Io in the network in...Ch. 5 - Use source exchange to find Io in the network in...Ch. 5 - Find RL in the network in Fig. P5.112 in order to...Ch. 5 - In the network in Fig. P5.113, find RL for maximum...Ch. 5 - Find RL for maximum power transfer and the maximum...Ch. 5 - Find RL for maximum power transfer and the maximum...Ch. 5 - Find RL for maximum power transfer and the maximum...Ch. 5 - Find RL for maximum power transfer and the maximum...Ch. 5 - Determine the value of RL in the network in Fig....Ch. 5 - Find RL for maximum power transfer and the maximum...Ch. 5 - Find the value of RL in the network in Fig. P5.120...Ch. 5 - Find the value of RL for maximum power transfer...Ch. 5 - Find the maximum power that can be transferred to...Ch. 5 - In the network in Fig. P5.123, find the value of...Ch. 5 - In the network in Fig. P5.124, find the value of...Ch. 5 - Find the value of RL in Fig. P5.125 for maximum...Ch. 5 - Calculate the maximum power that can be...Ch. 5 - Find RL for maximum power transfer and the maximum...Ch. 5 - Find the value of RL in Fig. P5.128 for maximum...Ch. 5 - A cell phone antenna picks up a call. If the...Ch. 5 - Some young engineers at the local electrical...Ch. 5 - Determine the maximum power that can be delivered...Ch. 5 - Find the value of the load RL in the network in...Ch. 5 - Find the value of RL in the network in fig. 5PFE-3...Ch. 5 - What is the current I in Fig. 5PFE4? a. 8 Ac. 0 A...Ch. 5 - What is the open-circuit voltage Voc at terminals...
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