Question

Consider the following statements:
Assertion (A): Norton current is equal to the short-circuit current at the output terminals.
Reason (R): Because Norton equivalent resistance is obtained by deactivating all independent sources and calculating the resistance seen from the output terminals.
The correct answer is:

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. (A) is correct, but (R) is not correct
• C. Both (A) and (R) are correct and (R) is not correct explanation of (A)
• D. (A) is not correct, but (R) is correct

Hint:

To test assertion-reason links, read them together using the word "because": "Norton current equals short-circuit current because Norton resistance is found by turning off sources..." This phrasing clearly shows a lack of logical connection, indicating that (R) is not the explanation for (A).

Answer 1

The Correct Option is C

Concept: Norton's Theorem states that any linear, bilateral active circuit containing independent and dependent sources can be simplified into an equivalent circuit featuring a single ideal current source connected in parallel with a single equivalent resistance.
• Norton Current (\(I_N\)): Calculated by placing a direct short circuit across the selected load terminals and determining the current that flows through that shorted path (\(I_N = I_{sc}\)).
• Norton Resistance (\(R_N\)): Determined by deactivating all independent sources within the network (replacing ideal voltage sources with short circuits and ideal current sources with open circuits) and measuring the equivalent internal resistance looking back into the open-circuited load ports. Note that \(R_N\) is identically equal to the Thevenin equivalent resistance (\(R_N = R_{th}\)).

Step 1: Evaluation of Assertion (A).
Assertion (A) states: "Norton current is equal to the short-circuit current at the output terminals." By definition, finding the Norton current requires shorting the output terminals and calculating the resulting terminal current. Thus, Assertion (A) is perfectly correct.

Step 2: Evaluation of Reason (R).
Reason (R) states: "Because Norton equivalent resistance is obtained by deactivating all independent sources and calculating the resistance seen from the output terminals." This statement describes the exact, standard protocol for determining the internal equivalent resistance of a linear active network. Thus, Reason (R) is also independently correct.

Step 3: Determining the explanatory link.
We now examine if Reason (R) forms the causative logical backbone explaining why Assertion (A) is true. The value of the short-circuit current (\(I_N\)) is dictated by the internal driving sources and topological impedances under load short conditions. It is conceptually independent of how one goes about finding the internal resistance (\(R_N\)). The statement in (R) explains the procedure for finding \(R_N\), not \(I_N\). Therefore, while both statements are correct, Reason (R) is not the correct explanation for Assertion (A).