(c) Let R₁ = R₂ = R3 = = 1. Find Us 1, Us2 that yield i1 = 1, 12 = -4,13 = 5. Is this possible? Why? (d) Repeat (c) with i₁ = 2, 12 = 0, i3 = -3. What is different this time?
(c) Let R₁ = R₂ = R3 = = 1. Find Us 1, Us2 that yield i1 = 1, 12 = -4,13 = 5. Is this possible? Why? (d) Repeat (c) with i₁ = 2, 12 = 0, i3 = -3. What is different this time?
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter13: Transmission Lines: Transient Operation
Section: Chapter Questions
Problem 13.20P
Related questions
Question
Parts C and D
![Consider a linear static circuit consisting of three resistors
and two independent voltage sources, as shown in Figure 1.
Let 11, 12, 13 represent the currents that flow through the re-
sistors, R₁, R2, R3 represent their resistances, and Us1, Us2
represent the voltages at the voltage sources.
(a) Using Ohm's and Kirchhoff's laws, express
11, 12, 13 as functions of R₁, R2, R3, Usl, Us2.
Write your result in the form of y = Ax, where
y = [1 12 13] and x = [vs1
US2] T.
(b) Let R₁
=
R₂ R3 = 1. Is it possible for two
distinct pairs of voltages, Us1, Us2 and v1, 2, to
produce the same currents i1, 12, 13? Why?
=
Vsl
+
W
R₁
M
R₂
R3
Figure 1
Vs2
(c) Let R₁ = R₂ = R3 = 1. Find Us1, Us2 that yield i₁ = 1, 12 = -4, 13 = 5. Is this possible? Why?
(d) Repeat (c) with i₁ = 2, 12 = 0, i3 = -3. What is different this time?
(e) Suppose, for safety reasons, the currents must satisfy 1 ≤ i ≤ 2, 1 ≤ i ≤ 2, and 0 ≤ i3 ≤ 1. On
a two-dimensional plane, sketch the set of all voltages Us1, Us2 that ensure these conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1df17bca-13fe-4084-844e-d71409422be9%2F746b3f03-735c-4eb6-9357-9d4e322eaebf%2Frkby8i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a linear static circuit consisting of three resistors
and two independent voltage sources, as shown in Figure 1.
Let 11, 12, 13 represent the currents that flow through the re-
sistors, R₁, R2, R3 represent their resistances, and Us1, Us2
represent the voltages at the voltage sources.
(a) Using Ohm's and Kirchhoff's laws, express
11, 12, 13 as functions of R₁, R2, R3, Usl, Us2.
Write your result in the form of y = Ax, where
y = [1 12 13] and x = [vs1
US2] T.
(b) Let R₁
=
R₂ R3 = 1. Is it possible for two
distinct pairs of voltages, Us1, Us2 and v1, 2, to
produce the same currents i1, 12, 13? Why?
=
Vsl
+
W
R₁
M
R₂
R3
Figure 1
Vs2
(c) Let R₁ = R₂ = R3 = 1. Find Us1, Us2 that yield i₁ = 1, 12 = -4, 13 = 5. Is this possible? Why?
(d) Repeat (c) with i₁ = 2, 12 = 0, i3 = -3. What is different this time?
(e) Suppose, for safety reasons, the currents must satisfy 1 ≤ i ≤ 2, 1 ≤ i ≤ 2, and 0 ≤ i3 ≤ 1. On
a two-dimensional plane, sketch the set of all voltages Us1, Us2 that ensure these conditions.
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