Solved: Show that the expressions for conductances as functions of the three Y

Chapter 3, Problem 3.64

(choose chapter or problem)

Show that the expressions for \(\Delta\) conductances as functions of the three Y conductances are

\(\begin{aligned}G_{a} & =\frac{G_{2} G_{3}}{G_{1}+G_{2}+G_{3}}, \\ G_{b} & =\frac{G_{1} G_{3}}{G_{1}+G_{2}+G_{3}}, \\ G_{c} & =\frac{G_{1} G_{2}}{G_{1}+G_{2}+G_{3}},\end{aligned}\)

where

\(G_{a}=\frac{1}{R_{a}}, \quad G_{1}=\frac{1}{R_{1}}, \quad \text { etc. }\)

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