Thevenin’s theorem is true for __________

Question

Examoogle · Accepted Answer

Linear networks

Explanation: Thevenin’s theorem states that any linear, two-terminal network containing multiple voltage sources, current sources, and resistors can be replaced by an equivalent circuit consisting of a single voltage source ($V_{th}$) in series with a single resistor ($R_{th}$). This principle relies strictly on the property of superposition, which only holds in linear systems where the response is proportional to the input.

Working Principle: The theorem works because, in a linear network, the relationship between voltage and current follows Ohm's law ($V = IR$). When we look into the terminals of a linear network, the internal voltage and impedance remain constant regardless of the external load connected, allowing for a simplified series representation.

Key Formulas: $V_{th} = V_{oc}$ — Thevenin voltage is equal to open-circuit voltage; $R_{th} = \frac{V_{oc}}{I_{sc}}$ — Thevenin resistance is the ratio of open-circuit voltage to short-circuit current

Key Points: The network must be linear, meaning elements like resistors, capacitors, and inductors must have constant values.; Non-linear elements (like diodes or transistors) violate the superposition principle, making Thevenin's theorem invalid.; The theorem is a fundamental tool for simplifying complex circuit analysis into a basic $V-I$ model.

Advantages: Simplifies analysis of complex networks by reducing them to a two-terminal circuit.; Easily determines current through a variable load resistor connected to the terminals.

Disadvantages: Requires knowledge of all internal component values or measurement of terminal conditions.

Applications: Analyzing power systems and communication networks.; Maximizing power transfer calculations via the Maximum Power Transfer Theorem.

Additional Info: Linearity ensures that $f(x_1 + x_2) = f(x_1) + f(x_2)$.. Option B is incorrect because non-linear elements cause the impedance to vary with voltage/current, negating the existence of a single $R_{th}$.

Answer: A is correct — Thevenin's theorem is strictly defined for linear networks where the principles of superposition and proportionality apply.

Exam Tip: Always verify if a circuit contains dependent sources or switches controlled by non-linear elements before applying Thevenin's theorem.

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