Question

The values of the currents $I_1$, $I_2$, and $I_3$ flowing through the circuit given below is

• A. $I_1 = -3$ A, $I_2 = 2$ A, $I_3 = -1$ A
• B. $I_1 = 2$ A, $I_2 = -3$ A, $I_3 = -1$ A
• C. $I_1 = 3$ A, $I_2 = -1$ A, $I_3 = -2$ A
• D. $I_1 = 1$ A, $I_2 = -3$ A, $I_3 = -2$ A
• E. $I_1 = 2$ A, $I_2 = -1$ A, $I_3 = -3$ A

Hint:

Always assign current directions first. Negative results indicate actual direction is opposite to assumed.

Answer 1

Answer: (E)

Concept:
Use Kirchhoff’s laws:
• KCL: Sum of currents at a junction is zero
• KVL: Sum of voltages in a loop is zero

Step 1: Apply KCL at node.
\[ I_2 = I_1 + I_3 \]

Step 2: Apply KVL in upper loop.
\[ 14 - 4I_2 - 10 - 6I_1 = 0 \]

Step 3: Apply KVL in lower loop.
\[ 10 - 6I_1 - 2I_3 = 0 \]

Step 4: Solve equations.
From equations: \[ I_1 = 2,\quad I_2 = -1,\quad I_3 = -3 \]