# Reciprocity Theorem: Statement, Explanation, Application, Limitation

The reciprocity theorem holds significant importance among the Network theorems and serves as a crucial element in the analysis of 2 port networks. The theorem utilized for the resolution of the provided electrical network or circuit is commonly referred to as the Network Theorem or Circuit Theorem in academic discourse.

## Reciprocity Theorem Statement

This theorem states that, “The ratio of excitation to response remains invariant in a reciprocal network with respect to an interchange between the points of application of excitation and measurement of response.”

## Explanation of Reciprocity Theorem

Consider a reciprocal network N as a black box with only two branches 1 and 2.

Suppose the source of emf E1 is inserted in branch 1 and it produces current I2 at branch 2.

Now ,if the point of application exciting E2 source is moved to branch 2 and the response I1 is measured at 1 ,the theorem asserts that ,

If current source Is1 is applied across branch 1 ,produces a potential difference(p.d) of V2 across branch 2,

Now,if current source Is2 is applied across branch 2 ,produces a potential difference(p.d) of V1 across branch 1,

It indicates that the voltage (V) and current(I) are mutually interchangeable and the ratio of V/I is called resistance or impedance.

## Steps for solving Reciprocity theorem

step 1:Branches is to be selected where reciprocity has to be established.

step 2:Current is to be calculated in the branch using any conventional network analysis method.

step 3:Voltage source or current source is interchanged between the branch which is selected.

step 4:current in the branch is calculated using any conventional network analysis method same as above.

step 5:Reciprocity theorem is verified i.e

Step 1:

step 2:

step 3:

Step 4:

step 5: Reciprocity theorem is verified i.e

## Application of Reciprocity theorem

• Applicable to bilateral linear network, time invariant network composed of positive elements.
• Provides great convenience in design and measurement problems.

## Limitations of Reciprocity theorem

• Not applied to network consists of any dependent source even if it is linear.
• Not applied to network of any time varying elements.
• Not applied to network of non-linear elements like diode, transistors etc.