Explanation:


Superposition theorem is a technique used to solve electrical circuits. It states that the response in any branch of a linear, time-invariant network is the sum of the responses caused by each individual source acting alone. Here, the key terms are linear, time-invariant network.

Linear Network:


A linear network is one that follows the principle of superposition. It means that the response of the network to a linear combination of inputs is equal to the linear combination of the responses to each input taken separately. The linear network obeys the principle of homogeneity, additivity, and shift invariance. The circuit elements like resistors, capacitors, inductors are linear elements. The linear network can be analyzed by using various techniques, such as superposition, Thevenin's theorem, Norton's theorem, etc.

Time-Invariant Network:


A time-invariant network is one that has the same response to a signal at any given time, regardless of when the signal is applied. It means that the network properties remain constant over time. The network elements are not time-dependent, and their values remain constant with respect to time. The circuit elements like resistors, capacitors, inductors are time-invariant elements. The time-invariant network can be analyzed by using Fourier series, Laplace transform, z-transform, etc.

Applicability of Superposition Theorem:


The superposition theorem is applicable only to linear, time-invariant networks. The theorem states that the response in any branch of the network is the sum of the responses caused by each individual source acting alone. The principle of superposition does not hold for nonlinear and time-varying circuits. In nonlinear circuits, the output is not proportional to the input, and in the time-varying circuits, the response changes with time. The superposition theorem is not valid for circuits containing dependent sources.

Conclusion:


In conclusion, the superposition theorem is applicable only to linear, time-invariant networks. The theorem can be used to simplify the analysis of complex circuits. The circuit elements like resistors, capacitors, and inductors are linear and time-invariant elements. The superposition theorem cannot be applied to nonlinear and time-varying circuits.