Short notes

Superposition Theorem Short Notes

A circuit with a 10V voltage source, a 2A current source, and three resistors (1 kΩ, 2 kΩ, 4.7 kΩ) looks messy to solve directly. Apply superposition: solve for the voltage across the 4.7 kΩ resistor with only the 10V source active (replace 2A source with open circuit), then with only the 2A source active (replace 10V with short circuit). Add the two partial voltages algebraically — if the first gives +3.2V and the second gives −1.8V, the total is 1.4V. That two-pass simplification is the entire method.

EEE, ECE, EI

How it works

Superposition principle: in a linear circuit with multiple independent sources, the response (current or voltage) at any element is the algebraic sum of responses due to each independent source acting alone, with all other independent sources set to zero (voltage sources → short circuit; current sources → open circuit). The principle holds only for linear elements — resistors, linear capacitors, inductors, and linear dependent sources. Dependent sources are never deactivated; they remain active in every partial circuit. Each partial circuit is solved using basic techniques: voltage divider, current divider, or mesh/nodal analysis.

Key points to remember

Superposition applies to voltages and currents, not directly to power — since P = V²/R = I²R, power is a quadratic function of current or voltage, so P_total ≠ P₁ + P₂ from individual sources. This is the most common mistake in exam answers. The theorem is valid only for circuits with linear bilateral elements. Superposition is most useful when independent sources are of different types (AC and DC, or two different frequencies) — it is the only clean way to handle mixed-frequency circuits where impedances differ. For n independent sources, n partial circuits must be solved, making superposition increasingly laborious compared to mesh/nodal analysis for large circuits.

Exam tip

The examiner always asks you to use superposition to find a current or voltage, followed by a power calculation — compute the total voltage or current first by superposition, then calculate power from the total, never by summing partial powers.

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