3739 Solve these exercises two ways:(a) Use the constraint to eliminate a variable.(b)

Chapter 13, Problem 39

(choose chapter or problem)

As illustrated in the accompanying figure on the next page, suppose that a current \(I\) branches into currents \(I_{1}\) , \(I_{2}\) , and \(I_{3}\) through resistors \(R_{1}\) , \(R_{2}\) , and \(R_{3}\) in such a way that the total power dissipated in the three resistors is a minimum. Find the ratios \(I_{1}\) : \(I_{2}\) : \(I_{3}\) if the power dissipated in \(R_{i}\) is \(I_i^2R_i(i=1,\ 2,\ 3)\) and \(I_{1}+I_{2}+I_{3}=I\) .

Equation Transcriptions:

Text Transcriptions:

I

I_1

I_2

I_3

R_1

R_2

R_3

I_1

I_2

I_3

R_i

I _ i ^2 R_i (i=1, 2, 3)

I_1 + I_2 + I_3 = I