Understanding Equivalent Circuits for Linear Networks

The question asks to identify which standard equivalent linear circuit represents a single voltage source connected in series with a resistance. This specific configuration is a fundamental representation used to simplify more complex linear circuits.

Thevenin Equivalent Circuit Explanation

The Thevenin theorem states that any linear electrical network containing only voltage sources, current sources, and resistances can be replaced at terminals AB by an equivalent combination of a single voltage source, $V_{Th}$, in series with a single resistance, $R_{Th}$.

• $V_{Th}$ is the open-circuit voltage at the terminals AB.
• $R_{Th}$ is the equivalent resistance seen from terminals AB when all independent sources are turned off (voltage sources short-circuited, current sources open-circuited).

Therefore, the Thevenin equivalent circuit is defined precisely as a voltage source in series with a resistance.

Comparing Options

Let's look at the other options provided:

• Norton's equivalent: The Norton theorem states that any linear electrical network can be replaced by an equivalent combination of a single current source, $I_N$, in parallel with a single resistance, $R_N$. This configuration (current source in parallel with resistance) is different from the voltage source in series with resistance described in the question.
• Maximum power equivalent circuit: The concept of maximum power transfer relates to the condition under which a load receives maximum power from a source. It involves matching the load resistance to the Thevenin or Norton equivalent resistance of the source circuit. It is not an equivalent circuit representation in the form of a source and series resistance.
• Reciprocal power circuit: This is not a standard term for an equivalent circuit used in basic linear circuit analysis in the same way as Thevenin or Norton equivalents. The concept of reciprocity relates to the transfer function between different parts of a circuit.

Based on the definitions, the linear circuit equivalent that consists of a single voltage source and a series resistance is the Thevenin equivalent circuit.