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18. 4 Ω 12 V 1₁ 12 Ω |24 V 13 www 8Ω.

18. 4 Ω 12 V 1₁ 12 Ω |24 V 13 www 8Ω.

College Physics
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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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
Transcribed Image Text: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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