Compensation Theorem

Compensation theorem is completely based on Ohm's law. Basically, when a current flows through a resistor, there would be a voltage drop across the resistor. This voltage drop opposes the source voltage V_s. Hence, the current flows through the following branch decreases. This decrease in current is compensated by replacing any one of the resistance with a voltage source V₁ which is represented by its internal resistance only. The current from the replaced voltage source V₁ is opposite to the direction of actual current in the network.

Explanation

Let us consider a network, whose supply voltage is 30V Due to voltage drop in a circuit resistance, the current flows through all branches are different. To compensate the circuit, the end resistor 4Ω is replaced by the 12V voltage supply(3A * 4Ω= 12V). A current from the 12V voltage supply flows in opposite to the direction of actual currrent.

Purpose of Compensation Theorem

To calculate the sensitivity of a bridge network. To analyse those networks where the values of the branch elements are varied and for studying the effect of tolerance on such values.