Question

The superposition theorem is essentially based on the concept of:

• A. duality
• B. reciprocity
• C. non-linearity
• D. linearity

Hint:

Superposition applies strictly to linear parameters such as voltage and current. It does not apply to Power calculations because power exhibits a non-linear quadratic relationship with current/voltage ($P = I^2R = \frac{V^2}{R}$).

Answer 1

The Correct Option is D

Concept: The Superposition Theorem states that in any linear bilateral network containing multiple independent sources, the overall response (voltage or current) in any branch is equal to the algebraic sum of the individual responses caused by each independent source acting alone, while all other independent sources are replaced by their internal impedances. For a system to be considered linear, it must satisfy two fundamental mathematical tenets: 1) Homogeneity (Scaling): $f(kx) = k \cdot f(x)$ 2) Additivity: $f(x_1 + x_2) = f(x_1) + f(x_2)$ These combined behaviors define a linear system. If a circuit contains non-linear elements (such as diodes or saturated transistors), superposition cannot be applied directly.

Step 1: Define system responses under multiple inputs.
Let an electrical system have inputs $x_1$ and $x_2$ corresponding to different independent power sources. The response function of the circuit can be expressed as $H(x)$.

Step 2: Map the additivity rule to circuit parameters.
Because the equations governing components like resistors ($V=IR$), inductors ($V=L\frac{di}{dt}$), and capacitors ($i=C\frac{dv}{dt}$) are linear differential operations, they obey: \[ H(x_1 + x_2) = H(x_1) + H(x_2) \] This mathematical step is exactly what justifies analyzing each source independently and then adding their outcomes together. Thus, the theorem relies entirely on linearity. This corresponds to Option (D).