Problem 10-8    Source:   Problem 2.42 - page 70 -   IRWIN, J. David - Book: Análise de Circuitos em Engenharia - 4ª edição - Ed. Pearson Education do Brasil - 2013.

In the circuit show in Figure 10-08.1, knowing that V_o = 12 V, calculate the value of R

Solution of the Problem 10-8

One of the problem data is that V_o = 12 V. Therefore, we can calculate the current flowing through the resistor of 4 ohms or i₃ . Thus, it is possible to calculate the potential value of e₁.

Let's first calculate the value of i₃.

Adding the 4 and 8 ohms resistors results in 12 ohms, because they are in series. As we know the value of i₃ we can calculate e₁. So:

We can calculate the value of i₁ knowing that the potential difference over resistor of 2 ohms is given by 48 - 36 = 12 volts. Thus:

We now need to apply the law of nodes to the node e₁ and calculate the value of i₂.

Substituting for the numerical values we have:

And as we know i₂ and e₁, we easily calculate R by simply applying the Ohm's law, or: