what is reciprocity theorem?

Reciprocity Theorem

Reciprocity 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 reciprocity 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.

 

Related terms:

Kirchhoff’s Laws

For more notes on Electrical Engineering:

https://www.notesforengineering.com/factory-lighting/

 

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