A current of 16 amperes branches into currents x, y, and z through resistors with resistences 8, 6, and 2 ohms as shown. I=x, R=8 I=y, R=6 1=16 amps I=z, R=2 Q 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.) x= y = amps amps z= amps
A current of 16 amperes branches into currents x, y, and z through resistors with resistences 8, 6, and 2 ohms as shown. I=x, R=8 I=y, R=6 1=16 amps I=z, R=2 Q 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.) x= y = amps amps z= amps
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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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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Transcribed Image Text:A current of 16 amperes branches into currents x, y, and z through resistors with resistences 8, 6, and 2
ohms as shown.
I=x, R=8
I=y, R=6
1=16 amps
I=z, R=2
Q
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.)
x=
y =
amps
amps
z=
amps
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