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

Question

Examoogle · Accepted Answer

Norton’s theorem

Explanation: Norton’s theorem is the dual of Thevenin’s theorem because it replaces a complex linear network with a constant current source in parallel with an internal resistance. While Thevenin’s theorem focuses on voltage-series representation, Norton’s theorem emphasizes current-parallel representation, satisfying the principle of source transformation in circuit analysis.

Working Principle: The principle relies on source transformation where a voltage source $V_{th}$ in series with $R_{th}$ can be converted into a current source $I_N = \frac{V_{th}}{R_{th}}$ in parallel with the same resistance $R_{th}$. This dual nature allows for simplified calculation of currents in load resistors for both voltage-dominated and current-dominated circuits.

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

Key Points: Thevenin's theorem reduces a circuit to a voltage source in series with an impedance.; Norton's theorem reduces a circuit to a current source in parallel with an impedance.; Both theorems rely on the linearity of the network components.; The internal impedance $Z_{th}$ (or $R_{th}$) remains identical for both theorems calculated at the same terminals.

Advantages: Reduces complex circuits to simple equivalent models.; Facilitates rapid analysis of variable load conditions.

Disadvantages: Only applicable to linear circuits.; Not suitable for circuits with non-linear components like diodes or transistors.

Applications: Load flow analysis in power systems.; Optimization of impedance matching in communication circuits.

Additional Info: Superposition theorem is a fundamental technique for linear circuit analysis rather than a dual transformation.. Maximum power transfer theorem dictates the conditions for maximum load power, not an equivalent circuit representation.. Millman’s theorem is specifically for simplifying parallel branches of voltage sources.

Answer: A is correct — Norton’s theorem acts as the dual to Thevenin’s theorem by applying current-parallel equivalence rather than voltage-series equivalence.

Exam Tip: Always remember that while the internal resistance $R_{th} = R_N$ is the same, the power delivered to the network changes depending on the configuration; apply these theorems strategically based on whether the load is in series or parallel.

Related Questions

Discussion (0)