GATE 2021 EE – Question 26
In the given circuit, for voltage $V_y$ to be zero, the value of $\beta$ should be ________. (Round off to 2 decimal places).
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Correct answer: -3.30 to -3.20
Explanation
With $V_y=0$ the node $V_x$ satisfies $\frac{6-V_x}{1}=\frac{V_x}{4}+\frac{V_x-0}{2}$, so $V_x=3.43$ V. At node $V_y$ the current $\frac{V_x}{2}=1.71$ A arrives from the $2\ \Omega$ resistor and $2$ A from the source. Both leave through the $3\ \Omega$ resistor: $\frac{0-\beta V_x}{3}=3.71$, so $\beta=-\frac{3\times3.71}{3.43}=-3.25$.