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Circuit elements are categorized as active and passive. Active elements generate energy, including voltage or current sources. Passive elements absorb energy, such as resistors, capacitors, and inductors. These independent and dependent sources provide power to circuits, while passive components consume or store it.

Linear elements satisfy both superposition and homogeneity principles. Superposition means the response to combined inputs equals the sum of individual responses. Homogeneity means multiplying the input by a constant multiplies the output by the same constant. Resistors, capacitors, and inductors are linear; thermistors are nonlinear.

The superposition principle states that if voltage v1 produces response i1 and voltage v2 produces response i2, then the element responds to the combined voltage with the combined response. This principle applies only to linear circuit elements and is fundamental for analyzing complex circuits with multiple sources.

Homogeneity means that multiplying the input of a linear device by any constant results in an equivalent multiplication of the output. For example, if doubling the input voltage doubles the output current, the element exhibits homogeneity. This property, combined with superposition, defines linear behavior.

Thermistors are nonlinear because they do not comply with the superposition and homogeneity principles that define linear elements. Their resistance changes significantly with temperature, causing their excitation-response relationship to deviate from linear behavior. This makes circuit analysis with thermistors considerably more complex.

Passive elements like resistors, capacitors, and inductors absorb energy from circuits rather than generate it. They are essential building blocks that control current flow, store energy, and dissipate power. Understanding passive element behavior is crucial for designing and analyzing circuit performance and efficiency.

Active elements generate energy and supply power to circuits, including voltage sources, current sources, batteries, and operational amplifiers. Passive elements absorb energy and cannot generate it independently. Circuits require both types: active elements provide power while passive elements control and utilize it effectively.