Thevenin resistance is found by

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shorting all voltage sources and opening all current sources

Explanation: Thevenin resistance ($R_{th}$) represents the equivalent resistance of a linear, bilateral network as seen from a specific pair of terminals. It is calculated by replacing all independent internal energy sources with their internal resistances while maintaining the network's passive topology.

Working Principle: An ideal voltage source has zero internal resistance, so it acts as a short circuit (0 V drop). An ideal current source has infinite internal resistance, acting as an open circuit (0 A flow). By nulling these sources, the circuit becomes purely passive, allowing the total equivalent resistance to be calculated using standard series and parallel combination techniques.

Key Formulas: $V_{source} = 0$ (Short circuit); $I_{source} = 0$ (Open circuit); $R_{th} = \left. \frac{V_{oc}}{I_{sc}} \right|_{independent \ sources = 0}$

Key Points: Independent voltage sources are replaced by a wire (0 V).; Independent current sources are replaced by a broken connection (0 A).; Dependent sources must remain in the circuit during the calculation of $R_{th}$.; Thevenin's theorem simplifies a complex linear circuit to a single voltage source in series with a resistor.

Advantages: Simplifies analysis of complex networks.; Useful for calculating maximum power transfer.; Efficient for analyzing a specific component connected to varying loads.

Disadvantages: Only applicable to linear, time-invariant circuits.; Does not apply directly if dependent sources depend on external load parameters.; Requires recalculation if the network topology changes.

Applications: Power system analysis for fault current calculation.; Electronics design for impedance matching.; Simplified modeling of battery and power supply equivalent circuits.

Additional Info: When dependent sources are present, $R_{th}$ is found by applying a test voltage source $V_t$ and measuring the resulting current $I_t$, then $R_{th} = V_t / I_t$.. Option D is the inverse of the correct procedure and would yield an incorrect impedance.

Answer: C is correct — Thevenin resistance is determined by nullifying all independent sources: short-circuiting all independent voltage sources and open-circuiting all independent current sources.

Exam Tip: Always remember: 'Voltage is Shorted, Current is Cut' (short for voltage, open for current) to easily recall the nulling process for both Thevenin and Norton equivalency.

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