Circuit theorems – What does Norton's theorem actually state? Statement: Norton's theorem provides a method for reducing any AC circuit to an equivalent that consists of an equivalent voltage source in series with an equivalent impedance. Decide if this statement is correct.

Introduction / Context:Norton's and Thevenin's theorems are dual tools for simplifying linear circuits at a specified frequency. Students often confuse which theorem yields a voltage source in series versus a current source in parallel. This item clarifies that distinction and when each applies in AC analysis with phasors and complex impedances.

Given Data / Assumptions:

• Linear, bilateral network seen from two terminals at a single frequency (phasor domain).
• Independent/dependent sources and complex impedances may be present.
• We want the form defined by Norton's theorem.

Concept / Approach:

Thevenin's theorem: replace the network by V_th in series with Z_th. Norton's theorem: replace the same network by I_n in parallel with Z_n, where Z_n = Z_th and I_n = V_th / Z_th. Therefore, the statement that Norton's theorem yields a voltage source in series is incorrect; that is precisely Thevenin's form.

Step-by-Step Solution:

Verification / Alternative check:

Convert between forms: series V_th–Z_th ↔ parallel I_n–Z_n using I_n = V_th / Z_th. Both predict identical terminal behavior, confirming the duality and the incorrectness of the statement.

Why Other Options Are Wrong:

“True” swaps the forms of the two theorems. The qualifiers about resistive networks or single frequency do not fix the misstatement; the topology (series vs. parallel) is still wrong for Norton.

Common Pitfalls:

Memorizing without understanding: Norton → current source in parallel; Thevenin → voltage source in series. Also forgetting that Z_th = Z_n.

Final Answer:

False.