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![Question 8
A current of 13 amperes branches into currents x, y, and z through resistors with resistences 2, 8, and 6
ohms as shown.
X =
y =
I=13 amps
Z=
< >
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 I'R, 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.)
Questis
I=x, R=2
I=y, R=8
I=2, R=6
m
Vide
amps
amps
amps](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c62a616-6a2f-456f-ac81-c6090d5022b3%2F8606f6c7-5466-4c6b-998e-2371c1deb0b2%2Fs80n1et_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 8
A current of 13 amperes branches into currents x, y, and z through resistors with resistences 2, 8, and 6
ohms as shown.
X =
y =
I=13 amps
Z=
< >
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 I'R, 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.)
Questis
I=x, R=2
I=y, R=8
I=2, R=6
m
Vide
amps
amps
amps
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