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A current of 6 amperes branches into currents x, y, and z through resistors with resistences 6, 4, and 3 ohms as shown. I=6 amps X = y = I=x, R=6 It is known that the current splits in such a way that the sum of the currents through the three resistors equals the initial current. The energy generated in each resistor is given by E = I2R, where I is the current in that resistor and R is the resistance. Use Lagrange multipliers to find the currents x, y, and z which will minimize the total energy generated. (It turns out that nature always splits the currents so that the total energy is minimized.) Z= I=y, R=4 I==, R=3 amps amps amps

A current of 6 amperes branches into currents x, y, and z through resistors with resistences 6, 4, and 3 ohms as shown. I=6 amps X = y = I=x, R=6 It is known that the current splits in such a way that the sum of the currents through the three resistors equals the initial current. The energy generated in each resistor is given by E = I2R, where I is the current in that resistor and R is the resistance. Use Lagrange multipliers to find the currents x, y, and z which will minimize the total energy generated. (It turns out that nature always splits the currents so that the total energy is minimized.) Z= I=y, R=4 I==, R=3 amps amps amps

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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A current of 6 amperes branches into currents x, y, and z through resistors with resistences 6, 4, and 3 ohms as shown. I=6 amps X = y = I=x, R=6 It is known that the current splits in such a way that the sum of the currents through the three resistors equals the initial current. The energy generated in each resistor is given by E = I2R, where I is the current in that resistor and R is the resistance. Use Lagrange multipliers to find the currents x, y, and z which will minimize the total energy generated. (It turns out that nature always splits the currents so that the total energy is minimized.) Z= I=y, R=4 I==, R=3 amps amps amps
Transcribed Image Text:A current of 6 amperes branches into currents x, y, and z through resistors with resistences 6, 4, and 3 ohms as shown. I=6 amps X = y = I=x, R=6 It is known that the current splits in such a way that the sum of the currents through the three resistors equals the initial current. The energy generated in each resistor is given by E = I2R, where I is the current in that resistor and R is the resistance. Use Lagrange multipliers to find the currents x, y, and z which will minimize the total energy generated. (It turns out that nature always splits the currents so that the total energy is minimized.) Z= I=y, R=4 I==, R=3 amps amps amps
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