1. Linearity Property:

    • Linearity describes a linear relationship between cause and effect in an element.
    • A resistor, for instance, follows Ohm’s law: (v = iR).
    • Linearity means that if the input (excitation) is multiplied by a constant, the output (response) is multiplied by the same constant.
    • Linear circuits consist of linear elements, linear dependent sources, and independent sources.


  2. Superposition Principle:

    • Consider one independent source at a time while turning off the others.
    • Replace voltage sources with short circuits and current sources with open circuits.
    • Dependent sources remain intact.
    • Find the output (voltage or current) due to each active source and combine them algebraically.

  3. Thevenin’s Theorem:

    • Any linear circuit can be replaced by an equivalent circuit with a single voltage source ((V_{\text{th}})) and a series resistor ((R_{\text{th}})).
    • Thevenin equivalent simplifies complex networks for analysis.

  4. Norton’s Theorem:

    • Similar to Thevenin’s, but replaces the circuit with a current source ((I_{\text{N}})) and a parallel resistor ((R_{\text{N}})).
    • Useful for simplifying circuits with current sources.

  5. Maximum Power Transfer Theorem:

    • To maximize power transfer from a source to a load, the load resistance should match the source resistance.
    • This ensures maximum power efficiency.

  6. Δ-Y and Y-Δ Conversions:

    • Convert between delta (Δ) and wye (Y) configurations for resistors in networks.
    • Useful when analyzing three-phase systems.

Remember, these theorems are powerful tools that simplify circuit analysis and design.