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GATE 2024 EC – Question 60

Networks, Signals and Systems · Two-Port Networks and Wye-Delta Transformation · 2 marks · Numerical answer

For the two port network shown below, the value of the $Y_{21}$ parameter (in Siemens) is ______.

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Correct answer: 1.49 to 1.51

Explanation

$Y_{21}=I_2/V_1$ with port 2 shorted ($V_2=0$). The junction node is then at 0 V, so $I_1=V_1/2$ flows into it. The dependent source has its "+" at the ground side, so the bottom of the 4 Ω is at $-8V_1$ and the current down the 4 Ω is $(0-(-8V_1))/4=2V_1$. KCL at the junction: $I_1+I_2=2V_1$, so $I_2=2V_1-\frac12V_1=1.5V_1$. Hence $Y_{21}=1.5$ S.