Problema 31-4    Source:    Problem prepared by the site's authors.

In the circuit shown in Figure 31-04.1 determine the values of V₁, V₂, I₁ and I₂ knowing that: Z₁₁ = 8, Z₁₂ = -12, Z₂₁ = -5 and Z₂₂ = 10

Solution of the Problem 31-4

As the values of the Z parameters were provided, we have the following equations:

Note that, according to the circuit shown in Figure 31-04.1, the resistor R₃ can be removed from the circuit as it is in parallel with a voltage source. That way, we can write the following equation for the left side of the quadripole.

So, replacing the  eq. 31-04.3 into eq. 31-04.1, we get:

And on the right side of the quadripole, we find the following relationship:

So, replacing the 31-4.5 into  31-4.2, we get:

Solving  eq. 31-04.6, we find the relationship:

Now substituting this relationship into the equation   eq. 31-04.4 and solving, we will find the value of I₂, that is:

And the value of I₁ is:

With this data, it is now possible to calculate V₁ and V₂.