Question

Find the value of current \(I\) in the circuit shown in the figure below.

• A. \(3\,A\)
• B. \(13\,A\)
• C. \(6\,A\)
• D. \(-13\,A\)

Hint:

At every junction, \[ \sum I_{\text{entering}} = \sum I_{\text{leaving}}. \] Solve junction currents one by one using KCL.

Answer 1

The Correct Option is B

Step 1: Use the junction rule.
Kirchhoff's current law says the total current flowing into any junction equals the total flowing out. We apply this junction by junction.

Step 2: Top-left junction.
A current of $15\,$A comes in and $8\,$A leaves along one branch. The remaining current in the top branch is \[ I_t=15-8=7\,\text{A}. \]

Step 3: Bottom-left junction.
Here $8\,$A comes in and $5\,$A leaves, so the bottom branch carries \[ I_b=8-5=3\,\text{A}. \]

Step 4: Bring the branches together.
The unknown $I$ is fed by both the top and bottom branches meeting at the output node.

Step 5: Add the contributions.
\[ I=I_t+I_b+3=7+3+3=13\,\text{A}. \] (the two side branches plus the remaining $3\,$A line combine to give the full current).

Step 6: State the result.
The current through the marked branch is $13\,$A.
\[ \boxed{I=13\,\text{A}} \]