GATE EC 2019 Set 1 — Question 14
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Network Theory → Circuit Fundamentals & Theorems → Reciprocity Theorem
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Question
Consider the two-port resistive network shown in the figure. When an excitation of is applied across Port 1, and Port 2 is shorted, the current through the short circuit at Port 2 is measured to be (see (a) in the figure).
Now, if an excitation of is applied across Port 2, and Port 1 is shorted (see (b) in the figure), what is the current through the short circuit at Port 1?
Now, if an excitation of is applied across Port 2, and Port 1 is shorted (see (b) in the figure), what is the current through the short circuit at Port 1?
Correct answer
(B) 1 A
Solution
According to the Reciprocity Theorem, for a linear, passive, and bilateral network, the ratio of excitation to response remains constant even if the positions of excitation and response are interchanged. In case (a):
Excitation at Port 1
Response at Port 2 (short-circuited)
Transfer conductance In case (b):
Excitation at Port 2
Response at Port 1 (short-circuited)
By reciprocity,
.
Excitation at Port 1
Response at Port 2 (short-circuited)
Transfer conductance In case (b):
Excitation at Port 2
Response at Port 1 (short-circuited)
By reciprocity,
.
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