Question

In the figure, the values of currents I\(_1\), I\(_2\) and I\(_3\) respectively are

• A. 6A, 1.5A and 1A
• B. 4A, 2.5A and 2A
• C. 4A, 2.5A and 1A
• D. 6A, 4.5A and 1.5A

Hint:

To avoid errors in nodal analysis, strictly follow the direction of the arrows given in the diagram. A current entering a node is positive, and leaving is negative in the sum.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question requires applying Kirchhoff's Current Law (KCL) at multiple junctions in a circuit branch to find unknown currents. KCL states that the sum of currents entering a junction equals the sum of currents leaving it.
Step 2: Key Formula or Approach:
Kirchhoff's Current Law:
\[ \sum I_{\text{in}} = \sum I_{\text{out}} \]
Step 3: Detailed Explanation:
Let's analyze the junctions from left to right as per the diagram:
At the first junction (left):
- Current entering from the top-left branch = \(5\text{A}\).
- Current leaving through the bottom-left branch = \(1\text{A}\) (as indicated by the arrow pointing away from the junction).
- Current leaving towards the right = \(I_1\).
Applying KCL: \(5 = 1 + I_1 \Rightarrow I_1 = 4\text{A}\).
At the second junction (middle-top):
- Current entering from the left = \(I_1 = 4\text{A}\).
- Current leaving towards the right = \(1.5\text{A}\).
- Current leaving downwards = \(I_2\).
Applying KCL: \(I_1 = 1.5 + I_2 \Rightarrow 4 = 1.5 + I_2 \Rightarrow I_2 = 2.5\text{A}\).
At the third junction (bottom-right):
- Current entering from the top = \(I_2 = 2.5\text{A}\).
- Current leaving towards the right = \(1.5\text{A}\).
- Current leaving downwards = \(I_3\).
Applying KCL: \(I_2 = 1.5 + I_3 \Rightarrow 2.5 = 1.5 + I_3 \Rightarrow I_3 = 1\text{A}\).
Comparing these values (\(I_1 = 4\text{A}, I_2 = 2.5\text{A}, I_3 = 1\text{A}\)) with the options, it matches option (3).
Step 4: Final Answer:
The values of currents are \(I_1 = 4\text{A}, I_2 = 2.5\text{A}\) and \(I_3 = 1\text{A}\).