Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Superposition theorem is applicable only to linear circuits. Reason (R) : The response in non-linear circuits is not directly proportional to excitation. In the light of the above statements, choose the most appropriate answer from the options given below :

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

Hint:

Superposition theorem is valid only for linear circuits because: \[ \text{Response} \propto \text{Input} \] Nonlinear circuits do not satisfy additivity and proportionality.

Answer 1

The Correct Option is A

Concept: The superposition theorem states that in a linear bilateral network containing multiple independent sources, the response in any element is equal to the algebraic sum of responses produced by each source acting independently. This theorem is valid only when: \[ \text{Response} \propto \text{Excitation} \] which is the fundamental property of linear circuits.

Step 1: Understanding Assertion (A). Assertion: \[ \text{Superposition theorem is applicable only to linear circuits} \] This statement is correct. In linear circuits:
• current varies proportionally with voltage,
• response due to multiple sources can be added algebraically,
• homogeneity and additivity properties hold. Therefore superposition theorem works correctly only in linear networks.

Step 2: Understanding Reason (R). Reason: \[ \text{The response in non-linear circuits is not directly proportional to excitation} \] This statement is also correct. Examples of nonlinear devices include:
• diodes,
• transistors operating in nonlinear region,
• saturating magnetic cores. In such circuits: \[ I \not\propto V \] Therefore responses cannot simply be added.

Step 3: Understanding why superposition fails in nonlinear circuits. Suppose: \[ V_1 \rightarrow I_1 \] and \[ V_2 \rightarrow I_2 \] In a nonlinear circuit: \[ (V_1+V_2)\neq(I_1+I_2) \] Thus additivity property fails. Hence superposition theorem becomes invalid.

Step 4: Checking the explanation relationship. Reason clearly explains Assertion because:
• superposition requires proportional response,
• nonlinear circuits do not satisfy proportionality. Hence:
• Assertion is correct,
• Reason is correct,
• Reason correctly explains Assertion.

Step 5: Selecting the correct answer. Therefore the correct option is: \[ \boxed{(1)} \]