## 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:**

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