Number 18 17-21 MODELS OF NETWORKSIn Probs. 17-19, using Kirchhoff's laws (see Example 2)and showing the details, find the currents:17.16 V18.and (b) that does include pivoting. Apply the programsto Probs. 11-14 and to some larger systems of yourchoice.19.2Ω4Ω4ΩEo12 VRx192wwR₁32 V2921₁VI₂12 Ω1₂R₁ QR3Wheatstone bridgeProblem 2012A24 V20. Wheatstone bridge. Show that if Rx/R3 = R₁/R₂ inthe figure, then I = 0. (Ro is the resistance of theinstrument by which I is measured.) This bridge is amethod for determining R. R₁, R2, R3 are known. R3is variable. To get Rx, make I = 0 by varying R3. Thencalculate R =R3R1/R2.600100089R₂ Q.V 400√x4wwwV 600x1x3A8001x2800Net of one-way streetsProblem 2112001100021. Traffic flow. Methods of electrical circuit analysishave applications to other fields. For instance, applyingfigure. Is the solution unique?22. Models of markets. Determine the equilibriumsolution (D₁ = S1, D2 = S₂) of the two-commoditymarket with linear model (D, S, P = demand, supply,price; index 1first commodity, index 2 = secondcommodity)=D₁ = 40 2P₁ - P2,S1D₂ = 5P₁ - 2P₂ + 16,S₂ = 3P₂ - 4.23. Balancing a chemical equation x₁C3H8 + x₂O₂ →X3CO2 + x4H₂O means finding integer x1, x2, X3, X4such that the numbers of atoms of carbon (C), hydrogen(H), and oxygen (O) are the same on both sides of thisreaction, in which propane C3H8 and O₂ give carbondioxide and water. Find the smallest positive integersX1, X 4.24. PROJECT. Elementary Matrices. The idea is thatelementary operations can be accomplished by matrixmultiplication. If A is an m × n matrix on which wewant to do an elementary operation, then there is amatrix E such that EA is the new matrix after theoperation. Such an E is called an elementary matrix.This idea can be helpful, for instance, in the designof algorithms. (Computationally, it is generally prefer-able to do row operations directly, rather than bymultiplication by E.)E₁(a) Show that the following are elementary matrices,for interchanging Rows 2 and 3, for adding −5 timesthe first row to the third, and for multiplying the fourthrow by 8.E2E3=10 00 00 101=-5 0 100 011 0 0 001 001000 000 0 0 110 0 004P₁ P₂ + 4,0 00 1 0000 8

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18. 4 Ω 12 V 1₁ 12 Ω |24 V 13 www 8Ω.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Number 18

17-21 MODELS OF NETWORKS
In Probs. 17-19, using Kirchhoff's laws (see Example 2)
and showing the details, find the currents:
17.
16 V
18.
and (b) that does include pivoting. Apply the programs
to Probs. 11-14 and to some larger systems of your
choice.
19.
2Ω
4Ω
4Ω
Eo
12 V
Rx
192
ww
R₁
32 V
292
1₁
VI₂
12 Ω
1₂
R₁ Q
R3
Wheatstone bridge
Problem 20
12A
24 V
20. Wheatstone bridge. Show that if Rx/R3 = R₁/R₂ in
the figure, then I = 0. (Ro is the resistance of the
instrument by which I is measured.) This bridge is a
method for determining R. R₁, R2, R3 are known. R3
is variable. To get Rx, make I = 0 by varying R3. Then
calculate R =
R3R1/R2.
600
1000
89
R₂ Q.
V 400
√x4
www
V 600
x1
x3
A800
1x2
800
Net of one-way streets
Problem 21
1200
11000
21. Traffic flow. Methods of electrical circuit analysis
have applications to other fields. For instance, applying
figure. Is the solution unique?
22. Models of markets. Determine the equilibrium
solution (D₁ = S1, D2 = S₂) of the two-commodity
market with linear model (D, S, P = demand, supply,
price; index 1
first commodity, index 2 = second
commodity)
=
D₁ = 40 2P₁ - P2,
S1
D₂ = 5P₁ - 2P₂ + 16,
S₂ = 3P₂ - 4.
23. Balancing a chemical equation x₁C3H8 + x₂O₂ →
X3CO2 + x4H₂O means finding integer x1, x2, X3, X4
such that the numbers of atoms of carbon (C), hydrogen
(H), and oxygen (O) are the same on both sides of this
reaction, in which propane C3H8 and O₂ give carbon
dioxide and water. Find the smallest positive integers
X1, X 4.
24. PROJECT. Elementary Matrices. The idea is that
elementary operations can be accomplished by matrix
multiplication. If A is an m × n matrix on which we
want to do an elementary operation, then there is a
matrix E such that EA is the new matrix after the
operation. Such an E is called an elementary matrix.
This idea can be helpful, for instance, in the design
of algorithms. (Computationally, it is generally prefer-
able to do row operations directly, rather than by
multiplication by E.)
E₁
(a) Show that the following are elementary matrices,
for interchanging Rows 2 and 3, for adding −5 times
the first row to the third, and for multiplying the fourth
row by 8.
E2
E3
=
1
0 0
0 0
0 1
0
1
=
-5 0 1
0
0 0
1
1 0 0 0
01 0
0
1
0
0
0 0
0
0 0 0 1
1
0 0 0
0
4P₁ P₂ + 4,
0 0
0 1 0
000 8

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