A current of 13 amperes branches into currents x, y, and z through resistors with resistences 2, 8, and 6 ohms as shown.

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A current of 13 amperes branches into currents x, y, and z through resistors with resistences 2, 8, and 6 ohms as shown.

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A Current Of 13 Amperes Branches Into Currents X Y And Z Through Resistors With Resistences 2 8 And 6 Ohms As Shown 1
A Current Of 13 Amperes Branches Into Currents X Y And Z Through Resistors With Resistences 2 8 And 6 Ohms As Shown 1 (43.82 KiB) Viewed 39 times
A current of 13 amperes branches into currents x, y, and z through resistors with resistences 2, 8, and 6 ohms as shown. 1=x, R=2 I=13 amps I=y, R=8 I=z, R=6 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= amps y = amps ZE amps
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