Reciprocity theorem

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Reciprocity Theorem Statement

Reciprocity theorem states that, for a network consisting of linear, bilateral elements, the ratio of excitation to response at an element due to a single excitation (source) is constant, even when the positions of
excitation (source) and response (element) are interchanged.

(or)

In any branch of a network, the current due to a single voltage source in the network is equal at the branch, when the source was originally placed at its position and when the source is placed in the branch in which the current was originally measured.

Note: The theorem generally fails in the presence of dependent sources.

Explanation of Reciprocity Theorem

Consider the following circuits for understanding the reciprocity theorem. Here the excitation (source) is V_S and R_L is load resistance connected via a passive network. Let the current measured at the load resistance R_L for the below circuit be I_L.

Circuit for reciprocity theorem 

Now interchange the positions of R_L and V_S as in the below. Now, if we measure the current in the interchanged R_L the current must be equal to I_L which is obtained in the previous circuit for the reciprocity theorem be satisfied.

Circuit for reciprocity theorem after interchanging

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Read also:
Thevenin's Theorem
Norton's Theorem