Problem 10-3    Source:   Problem 2.13 - page 64 -   IRWIN, J. David - Book: Análise de Circuitos em Engenharia - 4ª edição - Ed. Pearson Education do Brasil - 2013.

On the circuit show in Figure 10-03.1, determine:

a) The voltage V_o.

b) What power is supplied and/or received by the voltage source.

Solution of the Problem 10-3

Item a

In the Figure 10-03.2 we notice that the circuit that is highlighted in blue presents two series resistors ( 3 e 9 ohms ) which, in turn, are in parallel with the resistance of 4 ohms.

Therefore, by performing the calculation, the series results in 12 ohms and this, in parallel with 4 ohms, results an equivalent resistance of 3 ohms. In the Figure 10-03.3 we see how the simplified circuit was.

After simplifying the circuit we realize that all resistors are in series. Therefore, to calculate the R_total just add your values. So:

Now, by applying the Ohm's law, the value of i_total is:

With the value of i_total, we can calculate V_o, because by again applying the Ohm's law:

Item b

As in the whole circuit we have a single source of voltage it is obvious that this source will be the power supplier for the circuit. Therefore, its power must be negative, indicating that provides power, or:

Note that this power is exactly the power consumed by the whole circuit. If we multiply R_total by the square of i_total, we get the power dissipated by the resistors that make up the circuit, or:

It is known that the algebraic sum of all the powers involved in the circuit must be equal to ZERO, or: