Problem 10-23    Source:   Problem 12 - List of Problems Circuits I - School of Engineering Electrical Circuits - UFRGS - 2013 - Prof. Dr. Valner Brusamarello.

In the two circuits shown in Figure 10-23.1, R₁ and R₂ are the same. Knowing that in the first circuit V = (1/3) E, determine I in the second circuit.

Solution of the Problem 10-23

For the first circuit we can apply a resistive voltage divider and find a relationship between the resistors R₁ and R₂. So, applying eq. 10-02, we find:

Working algebraically this equation, we easily find that:

And to find the value of I just apply a current divider to the second circuit using eq. 10-05. Remembering that the numerator contains the value of the resistor where we do not want to calculate the current. In this case, we will enter the value of R₁, as we want to calculate the current in R₂. And we know that the current arriving at the node is 60 A. Like this:

Making the substitution R₁ = 2   R₂, we find: