GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 38 of 65

Marks: +1, -0

The equivalent impedance

z_{\eq}

for the infinite ladder circuit shown in the figure is

Solution:

Assume equivalent impedance = Z

Z=j 9+\;{z(j 4)}/{Z+j 4}

Z=\;{j 9(Z+j 4)+j 4 Z}/{Z+j 4}

Z^{2}+j 4 Z=j 9 Z-36+j 4 Z

Z^{2}-j 9 Z+36=0

(Z-j 12)(Z+j 3)=0

Z=j 12

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