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GATE 2018 EC – Question 35

Networks, Signals and Systems · Two-Port Networks and Wye-Delta Transformation · 1 mark · Numerical answer

The ABCD matrix for a two-port network is defined by:

$$\begin{bmatrix}V_1\\I_1\end{bmatrix}=\begin{bmatrix}A&B\\C&D\end{bmatrix}\begin{bmatrix}V_2\\-I_2\end{bmatrix}$$

The parameter $B$ for the given two-port network (in ohms, correct to two decimal places) is ________.

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Correct answer: 4.78 to 4.82

Explanation

$B=\frac{V_1}{-I_2}\Big|_{V_2=0}$. For this T-network with series arms $Z_1=Z_2=2\ \Omega$ and shunt arm $Z_3=5\ \Omega$, $B=Z_1+Z_2+\frac{Z_1Z_2}{Z_3}=2+2+\frac45=4.8\ \Omega$.