Problem 13-13    Source:   Problem created by the site's author.

For the circuit shown in Figure 13-13.1, using Kirchhoff's law, determine:

a) The value of the current i.

b) The voltage V_o.

Solution of the Problem 13-13   -    Kirchhoff's Method

Item a

Note that to solve this problem we added a current I circulating through the 12 Ω resistor. We call the node at the top of the circuit node a. So, looking at the circuit shown in Figure 13-13.1, we immediately recognize that:

Now we can apply Kirchhoff's law to node a, remembering that we adopted the convention of current leaving the node as positive and current entering the node as negative. Soon:

Rearranging algebraically, we find:

As all the components that form the circuit are in parallel, it is possible to write that:

Then, equating the equations eq. 13-13.1 and eq. 13-13.3, we obtain :

Then, substituting the equation eq. 13-13.4 into eq. 13-13.2, we obtain the value of i, or:

Item b

To calculate the value of V_o, simply use the equation eq. 13-13.3 and the value from i. Soon: