The superposition theorem states that: In a multi-source linear circuit, the current through or voltage across any element in the circuit is the sum of the currents or voltages produced by each source acting independently.
To calculate the contribution of each source, all the other sources must be removed. To remove the source, a voltage source is replaced by a short circuit or its internal resistance if given, and a current source is replaced by an open circuit or its parallel internal resistance if given.
When you sum the contributions from the sources, you should be careful to take their signs into account. It is best to assign a reference direction to each unknown quantity, if it is not already given.
The total voltage or current is calculated as the algebraic sum of the contributions from the sources. If a contribution from a source has the same direction as the reference direction, it has a positive sign in the sum; if it has the opposite direction, then a negative sign.
In order to use the superposition theorem with circuit currents and voltages, all of the components must be linear; that is, for all resistive components, the current must be proportional to the applied voltage (satisfying Ohm’s law).
Note that the superposition theorem is not applicable to power, since power is not a linear quantity. The total power delivered to a resistive component must be determined using the total current through or the total voltage across the component and cannot be determined by a simple sum of the powers produced by the sources independently.
The example below illustrates this principle. To enable studying, the solution has been written in the short cut form but if explanations are required, they will be given per request.
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