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AC Network Analysis

# Superposition Theorem

The superposition theorem for AC circuits is:
The current in any part of a network containing two or more sources can be calculated by analyzing the network one source at a time. The current due to each source is calculated for each branch of the network. The net current in each branch of the network is then the phasor sum of the respective branch currents due to each source.

The next example demonstrates application of the superposition theorem to AC circuits.

Example 1:
Solve the circuit of figure below with the superposition theorem.

Circuit for Example 1.

Solution:

1. The impedance network with Vb deleted, as shown in the figure below, can be solved for the branch currents due to Va only.

Example circuit with voltage Vb replaced by a short circuit (solution for currents due to Va)

2. The impedance network with Va short-circuited, as shown in the figure below, can be solved for the branch currents due to Vb only.

Example circuit with voltage Va replaced by a short circuit (solution for currents due to Vb)

3. The net branch currents are the phasor sums of the branch currents due to Va and Vb.