GATE EE 2016 Set 1 — Question 25
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Electric Circuits → Network Elements & Sources → R, L, C & M Elements
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Question
and 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?
Correct answer
(D) R_B = R_A / (1 + R_A)
Solution
By observing the two infinite ladder networks:
.
This matches option (D).
1.Circuit consists of a series resistor followed by a shunt resistor, repeating infinitely.
2.Circuit starts with a shunt resistor. Looking into the network after this first shunt resistor, we see a series resistor followed by a shunt resistor, which is exactly the definition of circuit .
Therefore, is the parallel combination of the first shunt resistor and the entire network:.
This matches option (D).
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