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.

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**

- https://byjusexamprep.com/reciprocity-theorem-i
- https://electrical-engineering-portal.com/resources/knowledge/theorems-and-laws/reciprocity-theorem
- https://circuitglobe.com/what-is-reciprocity-theorem.html