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Superposition Theorem | DC Network Analysis

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The Superposition Theorem is a powerful technique used in DC network analysis to simplify complex circuits and calculate the individual contributions of multiple independent sources to the overall response of the circuit. It can be applied to linear circuits containing resistors, voltage sources, and current sources.

The theorem states that in a linear circuit with multiple independent sources, the response (voltage across a specific element or current through it) can be determined by calculating the response caused by each source separately, while keeping all other independent sources turned off (replaced by short circuits for voltage sources and open circuits for current sources). Afterward, the total response is obtained by summing up the individual responses.

To apply the Superposition Theorem:

1. Turn off all but one independent source: For voltage sources, replace all other voltage sources with short circuits (zero volts), and for current sources, replace all other current sources with open circuits (zero current).

2. Analyze the circuit with only one active source: Use circuit analysis techniques like Ohm's law, Kirchhoff's laws, nodal analysis, or mesh analysis to find the voltage or current at the desired element.

3. Repeat the process: Repeat steps 1 and 2 for each independent source in the circuit, keeping only one source active at a time.

4. Sum the individual responses: Once you have calculated the voltage or current for each source, add them algebraically to obtain the total response at the desired element.

It's essential to remember that the Superposition Theorem is applicable only to linear circuits, which follow the principles of superposition. Non-linear components like diodes, transistors, etc., do not adhere to this principle, and the theorem cannot be directly applied to circuits containing such elements.
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