2.6:
Linear Circuits
Consider a resistor connected to a variable voltage source. As the voltage is increased, the corresponding current value is recorded.
The graphical representation reveals a linear relationship between the voltage and current.
Such circuits where circuit parameters remain consistent despite changes in voltage or current are called linear circuits.
Linear circuits are composed of linear elements or linear independent sources, and they satisfy homogeneity and additivity properties.
This principle can help in circuit modeling to predict the source current when the voltage drop across the load changes.
Initially, the current through the load resistor and the voltage drop across the top resistor are determined.
Next, the voltage drop across the central branch is obtained, which is used to calculate the current through that branch. Applying KCL gives the total source current.
When the load voltage changes, the new source current can be found by multiplying a constant with the old current and substituting the known values.
However, the linearity principle does not apply to the power calculation, as power has a square dependence on the current.
2.6:
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.