Problem 11-9    Source:    Adapted from the 1st test - Circuit Analysis I - Prof. Dr. Dênis Fernandes - PUCRS - 2018.

In the circuit show in Figure 11-09.1, calculate the voltages V_ab , v₁ and v₂.

Problem solving using Voltage Node Method   click here!

Solution of the Problem 11-9 -  Method of Transforming Sources

As we did in the previous exercise, let's turn the current source into two current sources, using the principle called source explosion . Thus, we have the circuit shown in the Figure 11-09.2.

Note that the two current sources are in parallel with resistors. Then we can make a new transformation of sources.

Let's turn current sources into voltage sources. Thus, we present the circuit in the Figure 11-09.3 already modified. Note that we have voltage sources in series with resistors. We can sum the values of the resistors in series, obtaining 6 ohms in series with the source of 6 volts and 3 ohms in series with the other source of 6 volts.

We can use more source transformation until we get a circuit that can no longer be reduced. In the Figure 11-09.4 we see the last two transformations we can make. With the right-hand circuit we can construct an equation to find the value of V_ab.

As indicated in the circuit, the circulating current by 2 ohms resistor has the value of 1 - (V_ab / 2). Then we can write:

In order to calculate, we find:

To calculate the values of v₁ and v₂, we will use the circuit shown in the Figure 11-09.5 as a reference.

Note that for the point 1 , we can write the following equation for the node voltage:

Remembering that V_ab = 1 and doing the calculation, we find:

And for the point 2, we can write the following equation:

And doing the calculation, we find:

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