miércoles, 9 de septiembre de 2015

Ley de Ohm III


Ohm's Law,
Example Three

Given the resistor arrangement shown below, prove that the relation between R1 and R2 must be R2=1.618R1 in order that the resistance of the system R be equal to R2.
R=R1+R1//R2=R1+R1R2/(R1+R2).
The condition is R=R2, so we do
R2=R1+R1R2/(R1+R2).
R1R2+R22=R12+R1R2+R1R2.
0= R22 - R1R2 - R12.
This is a second degree equation in R2, whose solution is R2= R1(1/2 ± )
Disregarding the minus sign we get R2 = 1.618R1

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