For a given passive linear network, the Thevenin equivalent circuit series resistance and Norton equivalent circuit parallel resistance are respectively R_TH and R_N. Which of the following is true

Explanation:

Analysis of Thevenin and Norton Equivalent Circuits

Definition: Thevenin and Norton equivalent circuits are techniques used in electrical engineering to simplify complex networks into more manageable forms for analysis. Thevenin's theorem represents a network as an ideal voltage source (V_TH) in series with a resistance (R_TH), while Norton’s theorem represents the same network as an ideal current source (I_N) in parallel with a resistance (R_N).

Key Relationship:

The resistances R_TH (Thevenin resistance) and R_N (Norton resistance) are always equal in value:

R_TH = R_N

This equivalence arises because both Thevenin and Norton transformations describe the same electrical network, but in different forms. The resistance remains unchanged during the transformation, as it represents the inherent impedance of the circuit.

Correct Option Analysis:

The correct option is:

Option 4: R_TH = R_N

This option is correct because the Thevenin equivalent resistance (R_TH) and Norton equivalent resistance (R_N) of a given passive linear network are always equal. This fundamental relationship ensures consistency in circuit transformations and analysis.