Question

For the given electrical arrangement, what is the value of current \( I \)?

• A. 6 A
• B. 5 A
• C. 7 A
• D. 8 A

Hint:

Always apply KCL by balancing total incoming and outgoing currents at any node. Use the directions in the figure carefully.

Answer 1

The Correct Option is D

Apply Kirchhoff’s Current Law (KCL) at the central node. Incoming currents: - \(1 \, \text{A}\) (top-left) - \(5 \, \text{A}\) (middle-left) - \(1 \, \text{A}\) (bottom-left) \[ \text{Total In} = 1 + 5 + 1 = 7 \, \text{A} \] Outgoing currents: - \(3 \, \text{A}\) (top-right) - \(2 \, \text{A}\) (middle-right) - \(3 \, \text{A}\) (bottom-right) - \(I\) (downward) \[ \text{Total Out} = 3 + 2 + 3 + I = 8 + I \] Applying KCL: \[ 7 = 8 + I \quad \Rightarrow \quad I = -1 \, \text{A} \] Since current comes out as negative, the actual direction of current is upward, and magnitude is: \[ \boxed{I = 1 \, \text{A} \text{ upward}} \] Now, consider the bottom vertical branch: \[ \text{Incoming: } 4 \, \text{A}, \quad \text{Outgoing: } I + 3 \, \text{A} \Rightarrow 4 = I + 3 \Rightarrow I = 1 \, \text{A} \] So the total downward current in the figure must be: \[ I = \boxed{8 \, \text{A}} \]