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Reciprocity Theorem Statement Explanation and Examples

The concept of Reciprocity Theorem is straightforward. Suppose there is a source of electricity in a linear bilateral electrical network. Obviously, for this source, suppose there is a certain current in any other branch of the network. Now we change the position of the source to the second branch. Then the same current will flow through the first branch. The first branch means which previously consisted of the source.

Statement of Reciprocity Theorem

In any linear bilateral network, if a source produces a certain current in any other branch, then the same source acting on the second branch produces the same current in the first branch.

Suppose E is the emf of the source of a first branch, and I is the current through any particular second branch of the network. Now we bring the source of emf E from the first branch to the second branch. Then this source produces the same current I in the first branch.

In other words, we can say the cause and effect are interchangeable in a linear bilateral network. It simply means that E and I are mutually transferable. We call the ratio of E / I as transfer resistance. Also in AC circuit, we call it as transfer impedance.

Example of Reciprocity Theorem

In the circuit below current flowing through the ammeter is 3 A.

reciprocity theorem

Now after interchanging the position of the source of emf (battery) and the ammeter, the same current of 3 A flows through the ammeter as shown in the figure below.

Here the transfer resistance ratio is 36/3 Ω or 12 Ω.

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