Problem 13-7    Source:   Adapted from Problem 3.73 - page 109 - ALEXANDER, Charles K. & SADIKU, Matthew N. O. - Book: Fundamentos de Circuitos Elétricos - 5ª edição - Ed. McGrawHill - 2013.

In the circuit show in Figure 13-07.1, determine the currents in the circuit, as well as power received and / or supplied by the source 2 V.

Solution of the Problem 13-7   -    Kirchhoff Method

Using the Kirchhoff law we know that in a closed loop the algebraic sum of the voltages must be equal to ZERO . In the figure above, we see the redesigned circuit where we show the direction (clockwise) of the currents I₁ , I₂, I₃ and I₄. Note that to solve this problem we must find four equations because there are four unknowns. Thus, we will use the program Octave to find the solution of the system of equations.

We can write the two equations for the meshes I₁ and I₂ of the circuit obeying the clockwise direction of the currents.

Let's write the other two equations for the meshes I₃ and I₄. So:

Therefore, we have a system of four equations with four unknowns, which will be solved using the Octave program, as stated above. So the solution is:

Now that we know the value of I₃ we can find the value of the power in the source of 2 volts, or:

As the current goes out by the positive pole then the source is supplying power to the circuit and, by convention, the power signal is negative .