- Compensation Theorem Definition: The compensation theorem is defined as replacing a resistor in a network with a voltage source equal to the voltage drop across that resistor.
- Ohm’s Law Connection: When current flows through a resistor, a voltage drop occurs, opposing the source voltage.
- Voltage Source Replacement: A resistor can be replaced by a voltage source with zero internal resistance and a voltage equal to the drop across the resistor.
- Imaginary Voltage Source: This replacement voltage source opposes the original network voltage.
- Example Network: In a network, replacing a resistor with a voltage source shows that current through other branches remains unchanged.
Concept of Compensation Theorem
This theorem is based on one basic concept. According to Ohm’s law, when current flows through any resistor, there would be a voltage drop across the resistor. This dropped voltage opposes the source voltage. Hence voltage drop across a resistance in any network can be assumed as a voltage source acting opposite to the source voltage. The compensation theorem depends upon this concept.
Explanation of Compensation Theorem
The theorem states that any resistor in a network can be replaced by a voltage source with zero internal resistance and a voltage equal to the voltage drop across the resistor caused by the current flowing through it.
This imaginary voltage source opposes the voltage of the replaced resistor. In a complex network, if a resistor R with current I has a voltage drop V = I.R, it can be replaced by a voltage source of V (= IR) that opposes the network voltage or current I direction.
Example of Compensation Theorem
Let’s understand the compensation theorem with an example.
Here in the network for 16V source, all the currents flowing through the different resistive branches are shown in the first figure. The current through the right most branch in the figure is 2A and its resistance is 2 Ω. If this right most branch of the network is replaced by a voltage source 
directed as shown in the second figure, then current through the other branches of the network will remain the same as shown in the second figure.
