Norton’s theorem is true for __________.

Question

Examoogle · Accepted Answer

linear networks

Explanation: Norton’s theorem states that any linear, bilateral two-terminal network can be replaced by an equivalent circuit consisting of a current source $I_N$ in parallel with a resistor $R_N$. This theorem relies on the principle of superposition, which is exclusively applicable to linear systems.

Working Principle: The theorem works by calculating the short-circuit current across the terminals to find $I_N$ and the equivalent resistance $R_N$ seen from the terminals with independent sources turned off. Because the proportionality of voltage and current is required for the superposition of circuit responses, non-linear elements (like diodes or transistors in active regions) violate the linearity conditions, rendering the theorem invalid for such components.

Key Formulas: $I_N = I_{SC}$ — Norton current is the short-circuit current between terminals; $R_N = R_{th} = \frac{V_{oc}}{I_{sc}}$ — Norton resistance equals Thevenin resistance

Key Points: Norton's theorem is the dual of Thevenin's theorem.; Linearity implies the circuit must follow Ohm's Law and the principle of Superposition.; The network must contain linear passive elements and independent/dependent sources.; Norton's theorem simplifies complex networks into a single current source and parallel resistor.

Advantages: Simplifies analysis of complex networks.; Useful for calculating current through a variable load impedance.

Disadvantages: Requires complex circuit reduction or mesh/nodal analysis to find parameters.

Applications: Power system analysis.; Electronics circuit design.; Determining maximum power transfer.

Additional Info: The superposition theorem is a prerequisite for Norton's theorem, and superposition is only defined for linear circuits.. Non-linear networks contain components like PN-junction diodes where $I = I_0(e^{\frac{qV}{kT}} - 1)$, which is non-linear.

Answer: A is correct — Norton’s theorem is exclusively applicable to linear networks where the relationship between voltage and current follows a linear proportionality.

Exam Tip: Remember that Thevenin's, Norton's, and Maximum Power Transfer theorems all require the network to be linear; always verify linearity before applying these simplification techniques in exams.

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