Superposition theorem is valid for _________

Question

Examoogle · Accepted Answer

Linear systems

Explanation: The Superposition theorem states that in any linear, bilateral network containing multiple independent sources, the voltage across or current through any element is equal to the algebraic sum of the voltages or currents caused by each independent source acting alone. This principle holds only for systems where the relationship between input and output is governed by linear differential equations.

Working Principle: The principle of superposition relies on two fundamental properties of linear systems: Additivity ($f(x_1 + x_2) = f(x_1) + f(x_2)$) and Homogeneity ($f(ax) = af(x)$). When calculating the response due to one source, all other independent voltage sources are replaced by their internal resistance (short-circuited) and independent current sources are replaced by their internal resistance (open-circuited).

Key Formulas: $f(a_1x_1 + a_2x_2) = a_1f(x_1) + a_2f(x_2)$ — The mathematical definition of a linear system.

Key Points: Independent voltage sources are short-circuited when turned 'off'.; Independent current sources are open-circuited when turned 'off'.; Dependent sources must remain active during all steps of the calculation.; The theorem cannot be applied to power calculations, as power is a non-linear function of current or voltage ($P = I^2R$).

Advantages: Simplifies analysis of circuits with multiple sources.; Allows isolation of the effect of each source individually.

Disadvantages: Inefficient for circuits with a very large number of sources.; Cannot be used for non-linear components like diodes or transistors.

Applications: Complex network analysis in power systems.; Simplifying circuit design in analog electronics.; Educational tool for understanding circuit behavior.

Additional Info: Non-linear systems (Option B) include components where parameters depend on the magnitude of voltage or current, such as semiconductor junctions, violating the linearity constraint.. The superposition theorem is a hallmark of linear time-invariant (LTI) systems.

Answer: A is correct — The superposition theorem is fundamentally predicated on the principle of linearity, requiring the output to be directly proportional to the input.

Exam Tip: Always verify that your circuit contains only linear elements before applying superposition; if you see a diode or a saturable inductor, use KVL/KCL or Nodal Analysis instead.

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