RECIPROCITY THEOREM

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This theorem applies to networks containing linear bilateral elements and a single voltage source or a single current source. This theorem may be stated as follows:

If a voltage source in branch A of a network causes a current of 1 branch B, then shifting the voltage source (but not its impedance) of branch B will cause the same current I in branch A.

It may be noted that currents in other branches will generally not remain the same. A simple way of stating the above theorem is that if an ideal voltage source and an ideal ammeter are inter-changed, the ammeter reading would remain the same. The ratio of the input voltage in branch A to the output current in branch B is called the transfer impedance.

Similarly, if a current source between nodes 1 and 2 causes a potential difference of V between nodes 3 and 4, shifting the current source (but not its admittance) to nodes 3 and 4 causes the same voltage V between nodes 1 and 2.

In other words, the interchange of an ideal current source and an ideal voltmeter in any linear bilateral network does not change the voltmeter reading.

However, the voltages between other nodes would generally not remain the same. The ratio of the input current between one set of nodes to the output voltage between another set of nodes is called the transfer admittance.

Explanation of Reciprocity Theorem

The location of the voltage source and the current source may be interchanged without a change in current. However, the polarity of the voltage source should be identical to the direction of the branch current in each position.

The Reciprocity Theorem is explained with the help of the circuit diagram shown below

The various resistances R₁, R₂, and R3 are connected in the circuit diagram above with a voltage source (V) and a current source (I). It is clear from the figure above that the voltage source and current sources are interchanged for solving the network with the help of the Reciprocity Theorem.

The limitation of this theorem is that it is applicable only to single-source networks and not to multi-source networks. The network where the reciprocity theorem is applied should be linear and consist of resistors, inductors, capacitors, and coupled circuits. The circuit should not have any time-varying elements.

RECIPROCITY THEOREM