Problem 12-9    Source:    Example A1.3 - page 798 -   HAYT, William H. Jr. , KEMMERLY, Jack E. , DURBIN, Steven M. -    Book:    Análise de Circuitos em Engenharia - Ed. McGraw Hill - 7ª Edição - 2008.

In the circuit show in Figure 12-09.1, calculate the voltage V_x.

Solution of the Problem 12-9   -    Nodal Voltage Method

Adapted from the solution presented by the book Source.

Looking at the circuit, we noticed that the potential difference between the points a - g it's the same as V_x. Between the points b - c we have a potential difference of 6 V_x. And between the points a - b we have a potential difference of 30 volts. Using these three information we can calculate the potential difference between the points c - g, that is, about the 5 ohms resistor. Therefore, we can write:

In this way, we can write the equation for the node g only in function of V_x and thus respond to what was requested by the problem. Knowing that the algebraic sum of all currents competing with the node g must be equal to zero, we have:

However, the solution to this equation is immediate and we find to V_x:

Any other method of solution would be much more laborious.