Replacing all other independent voltage sources with a short circuit
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For the multiple-sources circuits, the current from many sources can be
separated to be an individual current and also can be combined later. The overall
response (current or voltage) of the multiple-source circuit is the sum of each
individual source response when assume that the other sources are killed (make its
value to zero). For instance, killing the voltage source by short circuit, and killing the
current source by open circuit. This is the principle of superposition theory.
The superposition theorem states that in a linear circuit with several sources, the current and voltage for any element in the circuit is the sum of the currents and voltages produced by each source acting independently.
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The superposition theorem for electrical circuits states that for a linear system the response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where all the other independent sources are replaced by their internal impedances.