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# What is Reciprocity Theorem?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The **reciprocity theorem** is one of the important Network theorems, and it plays a vital role in 2 port networks. The theorem we use for solving the given electrical network/circuit is known as Network Theorem / Circuit theorem. Pair of terminals is known as a port. If the network has 2 such ports, then it is known as a 2-port network.

In this article, first, you will learn the Reciprocity theorem and its statement. Then, you will get to know how to apply the Reciprocity theorem for solving an electric circuit/network problem.

Table of content

## Reciprocity Theorem Statement

The reciprocity theorem states that in any linear and bilateral network or circuit having only one independent source, the ratio of response to excitation is constant even though the source is interchanged from the input terminals to output terminals.

Since we have two basic electrical quantities like voltage & current, we will get 4 possible ways regarding excitation and response of the electrical network in terms of voltage & current.

- The reciprocity theorem is applicable only to single-source networks.
- The reciprocity theorem is applicable only to the circuits containing dependent sources.

## Reciprocity Theorem Application

The reciprocity theorem is applied for network falling in the following 2 cases.

- Reciprocity Theorem to an electric circuit
- Reciprocity Theorem to a 2-port network

### Reciprocity Theorem to an Electric Circuit

In the following circuit, V_{S} is the input voltage and the current, and I flowing through the resistor R_{3} is the response or output current.

In the following circuit, we interchanged the position of input voltage and output current. In this circuit, V_{S} is the input voltage and the current, and I flowing through the resistor R_{1} is the response or output current.

In the first circuit, whatever the amount of current that flows through resistor R3, the same amount of current that will flow through resistor R_{1} in the second circuit because the magnitude and polarities of voltage, V_{S} are the same in both circuits & the output current direction is same in both circuits.

### Reciprocity Theorem to a 2-Port Network

As the name implies, a 2-port network consists of 2 ports, namely port 1 and port 2. In the following 2 port network, the voltage source, V_{S} is connected to port 1. This is the input voltage of the 2-port network. The current I_{2} flows through port 2, the response or output current of the 2-port network.

In the following 2-port network, the voltage source, V_{S}‘ is connected to port 2. This is the input voltage of the 2-port network. The current, I_{1}‘ flows through port 1, the response or output current of the 2-port network.

According to the Reciprocity theorem,

I_{1}‘V_{S}‘=I_{2}V_{S}

If V_{S}‘=V_{S}, then we will get I_{1}‘=I_{2}.

## Reciprocity Theorem Examples

Q1. Find the current, I of the circuit shown in fig(b) by using the Reciprocity theorem.

Ans: 1.5 A

Q2. Find the current, I of the 2-port network shown in fig(b) by using the Reciprocity theorem.

Ans: 0.2 A