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GATE 2016 EE SET -2 Question 27

\frac{V_{A}-V_{1}}{1}+\frac{V_{A}-V_{2}}{4}=0

\frac{4V_{A}-4V_{1}+V_{A}-V_{2}}{4}=0

\Rightarrow \frac{5V_{A}-5V_{1}}{4}=0

\Rightarrow 5V_{A}-4V_{1}-V_{2}=0

5V_{A}=4V_{1}+V_{2}        \Rightarrow V_{A}=\frac{4}{5}V_{1}+\frac{1}{5}V_{2} _______ (1)

\frac{V_{A}-V_{3}}{1}+\frac{V_{A}-V_{out}}{9}=0 \Rightarrow 9V_{A}-9V_{3}+V_{A}-V_{out}=0

10V_{A}-9V_{3}=V_{out} ________ (2)

Substituting equation (1) into equation (2)

10(\frac{4}{5}V_{1}+\frac{1}{5}V_{2})-9V_{3}=V_{out}

8V_{1}+2V_{2}-9V_{3}=V_{out}

 

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