Thevenin resistance is found by ________.

Question

Examoogle · Accepted Answer

shorting all voltage sources and opening all current sources

Explanation: Thevenin resistance ($R_{th}$) represents the equivalent resistance of a linear network as seen from a pair of terminals. To determine this value, all independent energy sources must be deactivated: independent voltage sources are replaced by short circuits (0 V), and independent current sources are replaced by open circuits (0 A).

Working Principle: The principle relies on the superposition property of linear networks. By nullifying independent sources, the network effectively becomes a passive resistive circuit. The equivalent resistance is then computed using series and parallel combination techniques relative to the open-circuited output terminals.

Key Formulas: $R_{th} = \frac{V_{oc}}{I_{sc}}$ — Definition based on open-circuit voltage and short-circuit current; $V_{source} \rightarrow 0 \Rightarrow$ Short Circuit; $I_{source} \rightarrow 0 \Rightarrow$ Open Circuit

Key Points: This method applies only to independent sources; dependent sources must remain in the circuit.; If dependent sources are present, $R_{th}$ is calculated as the ratio of test voltage $V_t$ to test current $I_t$ at the terminals ($R_{th} = \frac{V_t}{I_t}$).; The process effectively turns the active circuit into a passive one.

Advantages: Simplifies complex networks into a single resistor.; Allows for easy calculation of current for varying load resistances.

Disadvantages: Not directly applicable to non-linear circuits.; Becomes cumbersome if many dependent sources are present.

Applications: Circuit simplification for load analysis.; Power transfer theorem studies.

Additional Info: Option A is incorrect because current sources must be opened, not ignored.. Option B is incorrect because voltage sources must be shorted.. Option D is the inverse of the correct procedure.

Answer: C is correct — To find the Thevenin resistance, independent voltage sources are replaced by short circuits, and independent current sources are replaced by open circuits.

Exam Tip: Always remember: Voltage sources have internal resistance $R=0$ (Short), whereas ideal current sources have internal resistance $R=\infty$ (Open).

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