RECIPROCITY AND COMPENSATION THEOREM

RECIPROCITY THEOREM

In many electrical network it is found that if positions of voltage source and ammeter are interchanged, the reading of ammeter remains same. It is not clear to you. Let’s explain in details. Suppose a voltage source is connected to a passive network and an ammeter is connected to other part of the network to indicate the response. Now any one interchanges the positions of ammeter and voltage source that means he or she connects the voltage source at the part of the network where the ammeter was connected and connects 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 same in both cases. This is where the property of reciprocity comes in circuit. The particular circuit which has this reciprocal property is called reciprocal circuit. This type of circuit perfectly obeys reciprocity theorem.

COMPENSATION THEOREM

This theorem based on one basic concept. When electric current flows through any resistor, there would be a voltage drop across the resistor according to Ohm’s law. This dropped voltage opposes the source voltage. Hence voltage drop across an electric resistance in any network can be assumed as a voltage source acting opposite to the source voltage. The compensation theorem depends upon this concept.

According to this theorem, any resistance in a network may be replaced by a voltage source that has zero internal resistance and a voltage equal to the voltage drop across the replace resistance due to the current which was flowing through it. This imaginary voltage source is directed opposite to the voltage source of that replaced resistance. Think about a resistive branch of any complex network whose resistance value is R. Let’s assume current I flowing through that resistor R and voltage drop due to this current across the resistor is V = I.R. According to compensation theorem this resistor can be replaced by a voltage source whose generated voltage will be V ( = IR) and directed against the direction of network voltage or direction of current I.