Introduction and Explanation of Reciprocity Theorem
Reciprocity Theorem states that – In any branch of a network or circuit, the current due to a single source of voltage (V) in the network is equal to the current through that branch in which the source was originally placed when the source is again put in the branch in which the current was originally obtained.
What is Reciprocal Property?
In many electrical networks it is found that if the positions of voltage source and ammeter are interchanged, the reading of ammeter remains the same. It is not clear to you. Let’s explain it in details. Suppose a voltage source is connected to a passive network and an ammeter is connected to other parts of the network to indicate the response. Now anyone interchanges the positions of ammeter and voltage source that means he or she connects the voltage source to the part of the network where the ammeter was connected and connects an ammeter to that part of the network where the voltage source was connected. The response of the ammeter means current through the ammeter would be the same in both the cases. This is where the property of reciprocity comes in the circuit. The particular circuit that has this reciprocal property, is called reciprocal circuit. This type of circuit perfectly obeys reciprocity theorem.
Explanation of Reciprocity Theorem
The voltage source and the ammeter used in this theorem must be ideal. That means the internal resistance of both the voltage source and ammeter must be zero. The reciprocal circuit may be a simple or complex network. But every complex reciprocal passive network can be simplified into a simple network. As per reciprocity theorem, in a linear passive network, supply voltage V and output current I are mutually transferable.
Steps for Solving a Network Utilizing Reciprocity Theorem
Step 1 – Firstly, select the branches between which reciprocity has to be established.
Step 2 – The current in the branch is obtained using any conventional network analysis method.
Step 3 – The voltage source is interchanged between the branch which is selected.
Step 4 – The current in the branch where the voltage source was existing earlier is calculated.
Step 5 – Now, it is seen that the current obtained in the previous connection, i.e., in step 2 and the current which is calculated when the source are interchanged i.e., in step 4 are identical to each other.