GATE 2016 EE – Question 25

Electric Circuits · Network solution methods: KCL, KVL, Node and Mesh analysis · 1 mark · Multiple choice

$R_A$ and $R_B$ are the input resistances of circuits as shown below. The circuits extend infinitely in the direction shown. Which one of the following statements is TRUE?

Two infinite ladder networks. In circuit A, each section has a 2 Ω series resistor on the top rail and a 1 Ω shunt resistor, and $R_A$ is the resistance looking into the first section. Circuit B is the same ladder with an extra 1 Ω shunt resistor placed across the input terminals, and $R_B$ is the resistance looking in.

$R_A = R_B$
$R_A = R_B = 0$
$R_A < R_B$
$R_B = R_A / (1 + R_A)$

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Correct answer: (D) $R_B = R_A / (1 + R_A)$

Explanation

Circuit B is circuit A with a 1 Ω resistor in parallel across the input. So $R_B = 1 \parallel R_A = \frac{1 \times R_A}{1 + R_A} = \frac{R_A}{1 + R_A}$.