Problem 10E The electrical network shown in the accompanying figure is called a Wheatstone bridge. In this bridge, R2 and R4 are known resistances and R3 is a known resistance that can be varied. The resistance R1 is unknown and is to be determined by using the bridge. The resistance R5 represents the internal resistance of a voltmeter attached between nodes B and D. The bridge is said to be balanced when R3 is adjusted so that there is no current flowing in the branch between B and D. Show that, when the bridge is balanced, R1R4 = R2 R1. (In particular, the unknown resistance R1 can be found from R1 = R2R3/R4 when the bridge is balanced.)
Read moreTable of Contents
A.1
A.10
A.2
A.3
A.4
A.6
A.7
A.8
A.9
1.1
Introduction to Matrices and Systems of Linear Equations
1.2
Echelon Form and Gauss–Jordan Elimination
1.3
Consistent Systems of Linear Equations
1.4
Applications (Optional)
1.5
Matrix Operations
1.6
In this discussion of matrices and matrix operations (and later in the discussion of
1.7
vectors), it is customary to refer to numerical quantities as scalars.
1.8
Data Fitting, Numerical Integration, and Numerical Differentiation (Optional)
1.9
Matrix Inverses and Their Properties
2.1
Vectors in the Plane
2.2
Vectors in Space
3.1
Introduction
3.2
Vector Space Properties of Rn
3.8
Least-Squares Solutions to Inconsistent Systems, with Applications to Data Fitting
3.9
Theory and Practice of Least Squares
4.1
The Eigenvalue Problem for (2 × 2) Matrices
4.2
Determinants and the Eigenvalue Problem
Textbook Solutions for Introduction to Linear Algebra
Chapter 1.4 Problem 10E
Question
The electrical network shown in the accompanying figure is called a Wheatstone bridge. In this bridge, R2 and R4 are known resistances and R3 is a known resistance that can be varied. The resistance R1 is unknown and is to be determined by using the bridge. The resistance R5 represents the internal resistance of a voltmeter attached between nodes B and D. The bridge is said to be balanced when R3 is adjusted so that there is no current flowing in the branch between B and D. Show that, when the bridge is balanced, R1R4 = R2 R1. (In particular, the unknown resistance R1 can be found from R1 = R2R3/R4 when the bridge is balanced.)
Solution
The first step in solving 1.4 problem number 10 trying to solve the problem we have to refer to the textbook question: The electrical network shown in the accompanying figure is called a Wheatstone bridge. In this bridge, R2 and R4 are known resistances and R3 is a known resistance that can be varied. The resistance R1 is unknown and is to be determined by using the bridge. The resistance R5 represents the internal resistance of a voltmeter attached between nodes B and D. The bridge is said to be balanced when R3 is adjusted so that there is no current flowing in the branch between B and D. Show that, when the bridge is balanced, R1R4 = R2 R1. (In particular, the unknown resistance R1 can be found from R1 = R2R3/R4 when the bridge is balanced.)
From the textbook chapter Applications (Optional) you will find a few key concepts needed to solve this.
Visible to paid subscribers only
Step 3 of 7)Visible to paid subscribers only
Subscribe to view the
full solution
full solution
Title
Introduction to Linear Algebra 5
Author
Lee W. Johnson, R. Dean Riess, Jimmy T. Arnold
ISBN
9780201658590
The electrical network shown in the accompanying figure is
Chapter 1.4 textbook questions
-
Chapter 1: Problem 10 Introduction to Linear Algebra 5
-
Chapter 1: Problem 1 Introduction to Linear Algebra 5
Problem 1E (a) set up the system of equations that describes traffic flow; (b) determine the flows x1 , x2, and x3 if x4 = 100; and (c) determine the maximum and minimum values for x4 if all the flows are constrained to be nonnegative.
Read more -
Chapter 1: Problem 5 Introduction to Linear Algebra 5
Problem 5E determine the currents in the various branches.
Read more -
Chapter 1: Problem 2 Introduction to Linear Algebra 5
Problem 2E (a) set up the system of equations that describes traffic flow; (b) determine the flows x1 , x2, and x3 if x4 = 100; and (c) determine the maximum and minimum values for x4 if all the flows are constrained to be nonnegative.
Read more -
Chapter 1: Problem 6 Introduction to Linear Algebra 5
Problem 6E determine the currents in the various branches.
Read more -
Chapter 1: Problem 4 Introduction to Linear Algebra 5
Problem 4E find the flow of traffic in the rotary if x1= 600.
Read more -
Chapter 1: Problem 3 Introduction to Linear Algebra 5
Problem 3E find the flow of traffic in the rotary if x1= 600 .
Read more -
Chapter 1: Problem 7 Introduction to Linear Algebra 5
Problem 7E determine the currents in the various branches.
Read more -
Chapter 1: Problem 8 Introduction to Linear Algebra 5
Problem 8E determine the currents in the various branches.
Read more -
Chapter 1: Problem 9 Introduction to Linear Algebra 5
Problem 9E a) Set up (he system of equations that describes the traffic Mow in the accompanying figure. b) Show that the system is consistent if and only if a1 + b1 + c1 + d1 = a2 + b2 + c2 + d2.
Read more