Network theorems: Norton’s theorem states that any linear two-terminal network as seen by a load can be replaced by what simple equivalent?

Introduction / Context:Source transformations simplify complex networks for analysis and design. Norton’s and Thevenin’s theorems provide dual representations that make load calculations and circuit intuition straightforward.

Given Data / Assumptions:

• Linear, bilateral network (resistive or linear AC at a single frequency) observed at two terminals.
• Desire to replace the network facing a load with an equivalent source plus resistance.
• Standard definitions of Norton and Thevenin equivalents apply.

Concept / Approach:Norton’s theorem: any linear two-terminal network can be reduced to an ideal current source I_N in parallel with a resistance R_N. Thevenin’s dual form uses an ideal voltage source V_TH in series with R_TH. The parameters relate via V_TH = I_N * R_N and R_TH = R_N.

Step-by-Step Solution:Identify the target form: Norton equivalent.Recall definition: ideal current source in parallel with a resistance.Recognize duality with Thevenin form.Select “Ideal current source and parallel resistor.”

Verification / Alternative check:Perform a source transformation on a known Thevenin equivalent V_TH in series with R_TH to obtain I_N = V_TH / R_TH in parallel with R_TH; both yield identical terminal behavior for any load.

Why Other Options Are Wrong:A/C: These describe Thevenin or a mismatched form, not Norton. D: Current source in series with a resistor is not Norton’s canonical form for a two-terminal equivalent. E: Not applicable because a correct option is present.

Common Pitfalls:Confusing the series vs parallel resistor placement; mixing I_N with short-circuit current and R_N with deactivated-sources resistance without handling dependent sources correctly.

Final Answer:Ideal current source and parallel resistor