Problem 10-1    Source:   Problem elaborated by the author of the site.

In the circuit shown in Figure 10-01.1 , determine:

a) The currents i₁ , i₂ and i₃.

b) The voltage in the points e₁ e e₂.

c) Make a power balance of the circuit.

Solution of the problem 10-1

Item a

Initially, the value of i₁ must be calculated. To do so, note that the resistors of 10 and 20 ohms, in the figure above, are in series resulting in an equivalent resistance equal to 30 ohms. See in the Figure 10-01.2, how the circuit was.

In the Figure 10-01.2 to the side, note that the resistors of 20 e 30 ohms are in parallel, resulting in an equivalent resistance of 12 ohms. And this equivalent resistance is in series with that of 8 ohms. Thus, the circuit has been reduced to two resistors in series with the voltage source. So by applying the Ohm's law easily calculated i₁, that is:

From this moment, there are two different ways to calculate the values of i₂ and i₃.

Way 1

With the value of i₁, we can calculate the value of e₁ and from this result, by applying the Ohm law, we compute i₂ and i₃. Like this:

Thus, for the circuit above where the resistors of 20 and 30 ohms are connected in parallel to the point e₁, and knowing the value of e₁, just apply the Ohm's law to compute i₂ and i₃. So:

Note that the sum of i₂ with i₃ results in the value of i₁, as it should be.

Way 2

The other possible way is to apply a current divider using equation already studied and reproduced below. Note that a hypothetical resistor was used here R_a and we want the current (i_a) through it.

We know the total current i₁ that circulates in the circuit and also the value of the equivalent resistance of the parallel is known, that is, 12 ohms. Therefore, we can calculate the values of i₂ e i₃. So:

And so, through two different methods, the same values are found, showing that there is more than one way to calculate the results you want.

Item b

The value of e₁ has been calculated previously. To calculate e₂, applies to Ohm's law in the resistor of 20 ohms, where it circulates i₃, that is:

Item c