What is Reciprocity Theorem — The Engineering Knowledge

4 min readDec 28, 2022

Hello, readers welcome to the new post. In this lesson, we will learn What is Reciprocity Theorem. Reciprocity in the electrical system is a feature of circuitry that makes the relationship between volts and current at two points of the circuit. This thereon explains that the current at one point of the circuit due to the other point voltage is the same as the 2nd point current due to voltage at the first point.

This theorem is applicable to all types of passive circuits. Reciprocity theory is characteristic of the principle of reciprocity in electromagnetism. In this post, we will discuss this theorem works and solve practical examples. So let’s get started

Description of Reciprocity Theorem

How to Apply Reciprocity Theorem on Electrical Network

There are some steps involved to solve networks through the use of the reciprocity theorem.
First of all, select the branches of circuitry where the reciprocity theorm has to apply.
To find the value of current flowing in breach any circuit analysis technique like KVL, KCL, etc can be applied
In the next step interchanged the voltage sources between branches that we choose in the first step
Now find the current in the branch that has a voltage source before the reciprocity application
Now we can see that the current calculated in step two and the current find in step four where sources are interchanged have same value

Reciprocity Theorem Example with Solution

If we solve the above circuit and find the equivalent resistance value across the points C and D then we have
Req= [(2+1)II3]+2= 3.5 ohm
If we use this equivalent resistance and find the current I1
10/3.5= 2.86A
Now I2
I2=2.86 x3/(3+3)=1.43A
Now find I3
I3=2.83–1.43= 1.43A
Now solve other circuits

In this circuit voltage source is on the right side while the first circuit has on the left side.
If we solve for an equivalent circuit then we have
Req=(2II3)+1+2= 6/5+3=21/5=4.2ohm
Find I2=10/4,2=2.381A
Then we have I1=I2(3/(3+2)=2.381×3/5= 1.43A
So from these two circuitry solutions, we can find that the branch that has a source has a current 1.43 A in the first circuit and in the second circuit, the branch that has a voltage source also has a 1.43A current. So we have provided the reciprocity theorem

Where is the reciprocity theorem used?

What are the limitations of the reciprocity theorem?

Is reciprocity theorem valid for both DC and AC circuits?

Whether Antennas will satisfy the Reciprocity theorem?

That is all about the Reciprocity Theorem. All details have been explained. IF you have any queries ask here

Author: Henry

http://www.theengineeringknowledge.com

I am a professional engineer and graduate from a reputed engineering university also have experience of working as an engineer in different famous industries. I am also a technical content writer my hobby is to explore new things and share with the world. Through this platform, I am also sharing my professional and technical knowledge to engineering students.

Originally published at https://www.theengineeringknowledge.com on December 28, 2022.