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(b) Write down the augmented matrix [A|b] describing this system.

(b) Write down the augmented matrix [A|b] describing this system.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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please send solution for part b only handwritten solution accepted
1. This question about electrical circuits can be done, even if you have never seen electric circuits before. It uses Ohm's law about the current flowing through a conductor: the potential difference V (or voltage, measured in Volt) is equal to the resistance R (measured in Ohm) of the conductor times the current I flowing through the conductor, measured in Ampère. I The potential difference is V = IR. V ohms = volts / amps. I And it uses Kirchhoff's laws: Current Law For any node in an electrical circuit, the sum of currents flowing into that node equals the sum of currents flowing out of that node. Voltage Law In an electric circuit, the directed sum of the voltages around any closed loop equals zero. Consider the electric circuit 50 volts 11 ohms 7 ohms 3 ohms 30 volts I3 Kirchhoff's laws yield five equations constraining the currents in this system. Challenge (not assessed): Before you look at part (a), you might wish to attempt an educated guess at what these five equations are. (a) For each of the following equations, explain how it is derived from the circuit using a Kirchhoff law. 11 I + 7 13 = 80 amps (1) 312 + 713 = 30 amps (2) 11 I - 312 = 50 amps (3) I3 = I+ I2 (4) h+ I2 = I3 (5) (b) Write down the augmented matrix [A|b] describing this system. (c) Determine the ranks of A and [A|b], and interpret your answer. Hint: If you do not know how to interpret your answer, have a look at the Lecture Notes on rank. (d) Consider now the system consisting of the three equations (5), (2) and (3) (in this order). Write this system in the form Ai = 6, and solve it by finding the inverse of the matrix A. Hint: Remember that you need to use the methods from class. (e) What happens if you exchange the 30 Volt battery for one with voltage Vi and the 50 Volt battery for one with voltage V2? Write a few sentences detailing your understanding of how the discussion has to be modified, and then carry out the above computations in this modified setting. Be as specific as you can be.
Transcribed Image Text:1. This question about electrical circuits can be done, even if you have never seen electric circuits before. It uses Ohm's law about the current flowing through a conductor: the potential difference V (or voltage, measured in Volt) is equal to the resistance R (measured in Ohm) of the conductor times the current I flowing through the conductor, measured in Ampère. I The potential difference is V = IR. V ohms = volts / amps. I And it uses Kirchhoff's laws: Current Law For any node in an electrical circuit, the sum of currents flowing into that node equals the sum of currents flowing out of that node. Voltage Law In an electric circuit, the directed sum of the voltages around any closed loop equals zero. Consider the electric circuit 50 volts 11 ohms 7 ohms 3 ohms 30 volts I3 Kirchhoff's laws yield five equations constraining the currents in this system. Challenge (not assessed): Before you look at part (a), you might wish to attempt an educated guess at what these five equations are. (a) For each of the following equations, explain how it is derived from the circuit using a Kirchhoff law. 11 I + 7 13 = 80 amps (1) 312 + 713 = 30 amps (2) 11 I - 312 = 50 amps (3) I3 = I+ I2 (4) h+ I2 = I3 (5) (b) Write down the augmented matrix [A|b] describing this system. (c) Determine the ranks of A and [A|b], and interpret your answer. Hint: If you do not know how to interpret your answer, have a look at the Lecture Notes on rank. (d) Consider now the system consisting of the three equations (5), (2) and (3) (in this order). Write this system in the form Ai = 6, and solve it by finding the inverse of the matrix A. Hint: Remember that you need to use the methods from class. (e) What happens if you exchange the 30 Volt battery for one with voltage Vi and the 50 Volt battery for one with voltage V2? Write a few sentences detailing your understanding of how the discussion has to be modified, and then carry out the above computations in this modified setting. Be as specific as you can be.
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