Question

In an electric circuit, if 2A , 5 A and 4 A are the currents entering a junction and Ix , 2A and 3A are the currents leaving the junction, then the current value Ix is

• A. 2A
• B. 3A
• C. 4A
• D. 5A
• E. 6A

Hint:

KCL is just a common-sense check: Charge cannot accumulate at a junction. Whatever goes in must come out.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
Kirchhoff’s Current Law (KCL), also known as the Junction Rule, states that the algebraic sum of currents at any junction in a circuit is zero.
This is based on the law of conservation of electric charge.

Step 2: Key Formula or Approach:
\[ \sum I_{\text{entering}} = \sum I_{\text{leaving}} \]

Step 3: Detailed Explanation:
Sum of currents entering the junction:
\[ I_{\text{in}} = 2 \text{ A} + 5 \text{ A} + 4 \text{ A} = 11 \text{ A} \]
Sum of currents leaving the junction:
\[ I_{\text{out}} = I_x + 2 \text{ A} + 3 \text{ A} = I_x + 5 \text{ A} \]
Equating the two:
\[ 11 = I_x + 5 \]
\[ I_x = 11 - 5 = 6 \text{ A} \]

Step 4: Final Answer:
The value of current \( I_x \) is 6A.