- 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
The Compensation Theorem says you can replace a resistor by an ideal voltage source equal to its ohmic drop. Ohm’s law gives that drop: when current flows through a resistor, the drop opposes the source. So the voltage drop across a resistance can be treated as a voltage source acting against the original source. That replacement is the compensation theorem.
Explanation of Compensation Theorem
Any resistor in a network may be replaced by a voltage source with zero internal resistance whose voltage equals the voltage drop produced by the current in that resistor.
That replacement source opposes the drop that was across the resistor. If a resistor R carries current I, the drop is V = I.R. Replace the resistor with a source of V (= IR) whose polarity opposes current I.
Example of Compensation Theorem
The next two figures apply the theorem to a small resistive network.
The first figure shows the branch currents with a 16 V source. The right-hand branch carries 2 A through 2 Ω of resistance. Replace that branch with a voltage source 
oriented as in the second figure. The current in every other branch stays the same.
