Problem 31-1    Source:   Problem elaborated by the author of the site.

In the circuit shown in Figure 31-01.1, determine the parameters "Z".

Solution of the Problem 31-1

The Z parameters are given by the following equations:

We calculate Z₁₁ when we do I₂ = 0.Therefore, if there is no current flowing at the exit of the quadripole, then Z₁₁ will be the serial-parallel association of the resistors that make up the circuit, that is:

In the same way we will calculate Z₂₂, because in this case, we should have I₁ = 0. Then, looking at the output of the quadripole, let's calculate the resistance that we see when I₁ = 0. Then:

It's still missing to calculate Z₁₂ and Z₂₁. To calculate Z₁₂ we should have I₁ = 0 and we calculate the relation E₁ /I₂.So, setting a value for E₂ and calculating E₁ and I₂, as in the circuit shown in the Figure 31-01.2, we get:

Note that we arbitrate a convenient value for E₂ of value equal to 6 volts. Thus, we easily calculate I₂,whose value results in 2 A. From the analysis of the circuit and the values found so far, we can calculate E₁, finding the value of 4 volts. Soon:

To calculate Z₂₁ we will adopt the same procedure. For this, let's arbitrate E₁ = 8 volts. In the circuit shownin the Figure 31-01.3, we see the values found.

Note that it was obtained E₂ = 6 volts and I₁ = 3 A. Logo:

How can we perceive Z₁₂ = Z₂₁ and with this, it is concluded that the circuit is PASSIVE or RECIPROCAL.