Reciprocity Theorem: Statement, Explanation, Application, Limitation

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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
Reciprocity Theorem

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.

Also Read: Thevenins-theorem

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.

References

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