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, VS is the input voltage and the current, and I flowing through the resistor R3 is the response or output current.
In the following circuit, we interchanged the position of input voltage and output current. In this circuit, VS is the input voltage and the current, and I flowing through the resistor R1 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 R1 in the second circuit because the magnitude and polarities of voltage, VS 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, VS is connected to port 1. This is the input voltage of the 2-port network. The current I2 flows through port 2, the response or output current of the 2-port network.
In the following 2-port network, the voltage source, VS' is connected to port 2. This is the input voltage of the 2-port network. The current, I1' flows through port 1, the response or output current of the 2-port network.
According to the Reciprocity theorem,
If VS'=VS, then we will get I1'=I2.
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
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