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DC Network Analysis

# Superposition Theorem

Circuits containing two or more sources can be solved by applying Kirchhoff's laws and then solving the resulting equations simultaneously. On the other hand, it is possible to solve such circuits containing two or more sources by an Ohm's-law approach if each source is considered individually. This approach is referred to as the superposition theorem, which states:
In any network containing two or more sources, the current in any part of the network can be calculated by analyzing the network one source at a time with all other sources replaced by their internal resistances. The current is calculated for each source in each branch of the network. The net current in each branch of the network is the algebraic sum of the currents due to the separate sources.

The superposition theorem is best demonstrated by an example problem.

Example circuit.

Example:
Solve the circuit of figure above for the currents by applying the superposition theorem.

Example circuit with Va only.

Solution:

1. Solve for the respective currents due to source Va only, as shown in the figure above. The inactive source Vb is replaced by a wire (zero resistance), so we will get a parallel combination of resistors R2 and R3 in series with the resistor R1.

Example circuit with Vb only.

2. Solve for the respective currents due to source Vb only, as shown in the figure above.

3. The algebraic sum of the currents in Steps 1 and 2 is the current in the example circuit.