Consider the circuit shown in Figure 2. The magnitudes and directions of known c

Question

Consider the circuit shown in Figure 2. The magnitudes and directions of known currents are indicated by the numerical values and adjacent arrow heads respectively. The unknown currents are i_1, i_2, i_3, and i_4 and these are assumed to flow in directions illustrated in Figure 2. With reference to Figure 2, the current flowing into any one of the four nodes (labelled a, b, c, or d) in the circuit must be equal to the current flowing out of that node. For example, in the case of node a, this current balance equation can be written 30 + i_1 = i_3. Figure 2: Current flows in an electric circuit for Question 3. Using Equation 3 as a guide, write down the remaining three equations describing the current balance at each of the three remaining nodes (b, c, and d). Identify the matrix A and the vector b when the system of four equations in four unknowns is written in the form Ax = b where x =[i_1 i_2 i_3 i_4] Assuming you had access to Matlab, describe the steps you would take and the commands you would use in attempting to identify if this system of equations has a unique solution.

Explanation / Answer

Part A. Remaining three equations are

At Node B i1 + i2 = 20

At Node C i3 + i4 = 15

At Node D i2 + 10 = i4 +45

Part B. AX = b

Matrix A = 1 0 -1 0 Matrix B = -30

1 1 0 0 20

0 0 1 1 15

0 1 0 -1 35

Part C:

Enter coefficient matrix and the right side

Now, call linalg::matlinsolve to solve the system (AX = b)

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