Problem 13-6    Source:   Adapted from Exercise 3.7 - page 87 - ALEXANDER, Charles K. & SADIKU, Matthew N. O. - Book: Fundamentos de Circutos Elétricos - 5ª edição - Ed. McGrawHill - 2013.

For the circuit shown in the Figure 13-06.1, determine the currents in the circuit and the current value I_o, as well as the power received and / or supplied by the source 10 V.

Solution of the Problem 13-6   -    Kirchhoff Method

In this problem it should be noted that the meshes traveled by I₁ and I₂ have in common a source of current of 5A . As we saw in item 3, this characterizes a super-mesh (to review: Super-mesh Concept). In the same way, we have another super-mesh in relation to I₂ and I₃. As the two super-mesh intercept, as represented by the dotted line in green, in the figure above, one can write the equation for this super-mesh as follows:

Working algebraically with this equation and simplifying, one obtains:

In addition, for the node a we have the following relation:

And for the e node, we can write:

But from the circuit, we know thatI_o = - I₄. Then, the above equation can be written as:

And finally we can write the equation for the mesh where I₄ circulates, or:

To simplify this equation, we obtain:

Note that we get the four equations needed to find the four unknowns. This system of equations solved easily using the Octave program. Thus, the currents are:

As stated above, I_o = - I₄, then:

To complete the solution of the problem we will calculate the power supplied / received by the source voltage 10 volts . As the current I₄ enters the positive pole of the source, then it absorbs (receives) circuit power and its value, according to convention, is positive , or: