Which of the following is also known as the dual of Thevenin's theorem?

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Examoogle · Accepted Answer

Norton's theorem

Explanation: Norton's theorem is considered the dual of Thevenin's theorem because it transforms a linear two-terminal circuit into a parallel combination of a current source and an impedance, whereas Thevenin's theorem transforms it into a series combination of a voltage source and an impedance. Both theorems are fundamental tools in circuit analysis used to simplify complex linear networks for easier load calculation.

Working Principle: The principle of duality in network analysis states that for every circuit parameter, there is a dual: current source corresponds to voltage source, parallel connection corresponds to series connection, and conductance (G) corresponds to resistance (R). By applying Norton's theorem, we replace the Thevenin voltage $V_{th}$ in series with $R_{th}$ with a current source $I_N = \frac{V_{th}}{R_{th}}$ in parallel with $R_{th}$.

Key Formulas: $I_N = \frac{V_{th}}{R_{th}}$ — Norton current in terms of Thevenin parameters; $R_N = R_{th}$ — Norton resistance equals Thevenin resistance

Key Points: Thevenin's theorem uses a voltage source in series with a resistor.; Norton's theorem uses a current source in parallel with a resistor.; Both theorems rely on the linearity of the network components.; The open-circuit voltage ($V_{oc}$) is equal to $V_{th}$ and the short-circuit current ($I_{sc}$) is equal to $I_N$.

Advantages: Simplifies analysis of complex networks by reducing them to two-terminal equivalents.; Allows for rapid calculation of current/voltage for varying load impedances.

Disadvantages: Requires identifying internal resistance which can be difficult in complex multi-source active networks.

Applications: Power system analysis for fault current calculation.; Optimizing load matching in electronic circuit design.

Additional Info: Superposition theorem is a method of analysis, not a source equivalence.. Maximum power transfer theorem describes load conditions for power delivery, not circuit reduction.. Millman's theorem is a simplification technique for parallel voltage sources.

Answer: A is correct — Norton's theorem is the dual of Thevenin's theorem, as it replaces a voltage source circuit with a current source circuit.

Exam Tip: Always remember that $R_{th} = R_N$; calculating the internal resistance of a network remains the same regardless of whether you are finding a Thevenin or Norton equivalent.

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