According to Kirchhoff's Junction Rule, if three currents meet at a junction such that $I_1$ enters the junction, while $I_2$ and $I_3$ leave the junction, and $I_1$ = $5$ A, $I_2$ = $2$ A, what is the magnitude of the current in the upper branch, $I_3$?

• A. $5$ A
• B. $2$ A
• C. $7$ A
• D. $3$ A

Answer: (D)

Verified step by step guidance

1. Recall Kirchhoff's Junction Rule, which states that the total current entering a junction must equal the total current leaving the junction. Mathematically, this can be written as \(\sum I_{in} = \sum I_{out}\).
2. Identify the currents entering and leaving the junction. Here, \(I_1 = 5\) A enters the junction, while \(I_2 = 2\) A and \(I_3\) leave the junction.
3. Set up the equation based on Kirchhoff's Junction Rule: \(I_1 = I_2 + I_3\).
4. Rearrange the equation to solve for the unknown current \(I_3\): \(I_3 = I_1 - I_2\).
5. Substitute the known values into the equation: \(I_3 = 5\ \text{A} - 2\ \text{A}\) to find the magnitude of the current in the upper branch.