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 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.
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