q what do you mean by superposition and

Question

Q. What do you mean by Superposition and linearity?

Mathematically a function is said to be linear if it satisfies two properties: homogeneity (proportionality or scaling) and additivity (superposition),

f (K_x) = Kf (x) (homogeneity)

where K is a scalar constant, and

f (x₁ + x₂) = f (x₁) + f (x₂) (additivity)

Linearity requires both additivity and homogeneity. For a linear circuit or system in which excitations x1 and x2 produce responses y₁ and y₂, respectively, the application of K₁x₁ and K₂x₂ together (i.e., K₁x₁ + K₂x₂) results in a response of (K₁y₁ + K₂y₂), where K₁ and K₂ are constants. With the cause-and-effect relation between the excitation and the response, all linear systems satisfy the principle of superposition. A circuit consisting of independent sources, linear dependent sources, and linear elements is said to be a linear circuit. Note that a resistive element is linear. Capacitors and inductors are also circuit elements that have a linear input-output relationship provided that their initial stored energy is zero. Nonzero initial conditions are to be treated as independent sources.