Linear Circuits

A linear circuit is characterized by its output having a direct proportionality to its input, adhering to the linearity property, which encompasses the principles of homogeneity (scaling) and additivity. Homogeneity dictates that when the input, also referred to as the excitation, is multiplied by a constant factor, the output, known as the response, is correspondingly scaled by the same constant factor. For instance, if the current is multiplied by a constant 'k,' the voltage likewise experiences an increase of 'k' times.

The additivity property stipulates that the response to a sum of inputs equals the sum of responses to each individual input applied separately. In essence, this property enforces that the circuit's behavior remains consistent even when multiple inputs are combined.

Notably, a resistor is classified as a linear element because it satisfies both the homogeneity and additivity properties within its voltage-current relationship. Generally, a circuit is considered linear if and only if it demonstrates both additivity and homogeneity characteristics. Such linear circuits exclusively comprise linear elements, linear dependent sources, and independent sources.

Conversely, the expression for power, which is defined as the ratio of the square of voltage to resistance, constitutes a quadratic function and, therefore, falls under the category of nonlinearity within the context of circuit analysis.