A current of 9 amperes branches into currents x, y, and z through resistors with resistences 9, 4, and 2 ohms as shown.
I=x, R=9
I=9 amps
I=y, R=4
I=z, R-2
a
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 = l’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.)
x =
amps
y =
amps
ZE
amps