Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The Kirchhoff's current law states that sum of currents entering at any node is equal to the sum of currents leaving that node. Reason (R): The Kirchhoff's current law is based on the law of conservation of charge. 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:

Kirchhoff's Current Law: \[ \sum I=0 \] at a node. KCL is derived from: \[ \text{Law of Conservation of Charge} \]

Answer 1

The Correct Option is A

Concept: Kirchhoff’s Current Law (KCL) is one of the fundamental laws of electrical circuits. It states: \[ \sum I_{entering}=\sum I_{leaving} \] or equivalently: \[ \sum I =0 \] at any node. This law originates from: \[ \text{Conservation of Charge} \] which states that electric charge can neither be created nor destroyed.

Step 1: Analyze Assertion (A). Assertion states: Sum of currents entering a node equals sum of currents leaving the node. This is exactly the statement of Kirchhoff’s Current Law. Therefore: \[ (A)\text{ is correct} \]

Step 2: Analyze Reason (R). Reason states: KCL is based on conservation of charge. This statement is also correct. At a circuit node:
• Charge cannot accumulate indefinitely.
• Total incoming charge per second must equal outgoing charge per second. Thus KCL directly follows from conservation of electric charge. Hence: \[ (R)\text{ is correct} \]

Step 3: Determine the relationship between Assertion and Reason. The reason correctly explains the assertion because:
• Conservation of charge is the physical principle behind KCL. Hence:
• Both Assertion and Reason are correct.
• Reason correctly explains Assertion.

Step 4: Write the final answer. Therefore, the correct option is: \[ \boxed{(A)\ \text{Both (A) and (R) are correct and (R) is the correct explanation of (A)}} \]