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A current of 10 amperes branches into currents x, y, and z through resistors with resistences 3, 8, and 7 ohms as shown. X = y = I=10 amps Z = I=x, R=3 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.) I=y, R=8 I=z, R=7 amps amps amps

A current of 10 amperes branches into currents x, y, and z through resistors with resistences 3, 8, and 7 ohms as shown. X = y = I=10 amps Z = I=x, R=3 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.) I=y, R=8 I=z, R=7 amps amps amps

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A current of 10 amperes branches into currents x, y, and z through resistors with resistences 3, 8, and 7 ohms as shown. X = I=10 amps y = 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 = 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.) I=x, R=3 Question Help: I=y, R=8 I=z, R=7 Video amps amps amps
Transcribed Image Text:A current of 10 amperes branches into currents x, y, and z through resistors with resistences 3, 8, and 7 ohms as shown. X = I=10 amps y = 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 = 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.) I=x, R=3 Question Help: I=y, R=8 I=z, R=7 Video amps amps amps
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