Electronics Engineering (ELEX) Board Practice Exam

What is the value of currents I₁, I₂, and I₃ flowing in the first, second, and third mesh respectively?

1. 0.96 A, -1.73 A, 1.54 A

2. 1.54 A, -0.189 A, -1.195 A

3. 1.00 A, -0.50 A, 0.50 A

4. 1.73 A, 0.96 A, -1.54 A

The correct answer is: 1.54 A, -0.189 A, -1.195 A

To understand the selection of currents I₁, I₂, and I₃ for the meshes in the circuit, it’s important to consider the fundamental principles of circuit analysis, particularly mesh analysis or mesh current method. This technique involves writing Kirchhoff's Voltage Law (KVL) equations for each independent loop or mesh in the circuit, allowing us to find the unknown mesh currents. In this context, the chosen values of 1.54 A for I₁, -0.189 A for I₂, and -1.195 A for I₃ indicate specific behaviors of the currents in relation to the circuit components, such as resistors, voltage sources, and the orientation of the mesh currents. The positive value for I₁ suggests that this current flows in the assumed direction defined during the mesh analysis. The negative values for I₂ and I₃ imply that these currents are flowing in the opposite direction to how they were initially assumed. This can occur when the assumed current direction encounters a voltage drop that is greater than the potential rise (such as from a voltage source), leading to the actual current flowing in the reverse direction. This set of currents likely satisfies all the KVL equations formed from the meshes, which require that