Q18Basic Electrical Engineering

Application of Superposition Theorem: The Superposition Theorem simplifies complex multi-source DC networks. It dictates that the total current flowing through a specific branch (like the 40-ohm resistor) is the algebraic sum of the currents produced by each source acting independently.

Step-by-Step Procedure:

• 1. Activate Source 1 Only: Deactivate all other independent sources. Voltage sources are replaced by short circuits (wires), and current sources are replaced by open circuits (breaks). Analyze this simplified circuit using standard mesh analysis or series-parallel reduction to find the current $I_1$ flowing through the 40-ohm resistor. Note its direction.
• 2. Activate Source 2 Only: Restore the second source and deactivate the first source (and any others) using the same short/open rules. Analyze the newly formed simplified circuit to find the current $I_2$ through the 40-ohm resistor. Note its direction.
• 3. Algebraic Summation: Combine the partial currents. If $I_1$ and $I_2$ flow in the exact same direction through the 40-ohm resistor, they are added ($I_{total}=I_1+I_2$). If they flow in opposite directions, they are subtracted from one another ($I_{total}=I_1-I_2$ or vice versa), and the final current flows in the direction of the larger partial current.

This method completely eliminates the need to solve simultaneous equations for the entire network all at once.