The GATE Grind

GATE 2018 EE – Question 42

Electric Circuits · Network Elements: Ideal voltage and current sources, dependent sources, R, L, C, M elements · 2 marks · Multiple choice

The equivalent impedance $Z_{eq}$ for the infinite ladder circuit shown in the figure is

Diagram for GATE 2018 EE question 42
  1. $j12\ \Omega$
  2. $-j12\ \Omega$
  3. $j13\ \Omega$
  4. $13\ \Omega$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $j12\ \Omega$

Explanation

Each shunt branch is $j5-j1=j4\ \Omega$. Let $Z_{eq}=jx$. Then $jx=j9+\frac{j4\cdot jx}{j4+jx}$ with the series $j9$ and the parallel combination, which gives $(x-9)(x+4)=4x$, i.e. $x^2-9x-36=0$ and $x=12$. So $Z_{eq}=j12\ \Omega$.