Find V0 in the network in Fig. P3.12 using nodal analysis.

#### Solution:

Show me the final answerâ†“

Let us label our nodes and currents as follows:

As there are two voltage sources, the blue node and the green node will be kept at a certain voltage difference between the reference node (ground node) and the selected node. In other words, the blue node is 12 v as there is a 12 voltage source supply power, and the green node will be kept at 6 v due to the 6 v power supply directly corrected.

Looking at the orange node, V_1, we can write a KCL equation.

We can write these currents in terms of voltage and resistance by using I=\dfrac{V}{R}.

\dfrac{V_1}{6000}+\dfrac{V_1-6}{12000}+\dfrac{V_1-12}{6000}=0

Solving for V_1 gives us:

From the diagram, we see that V_0 is the difference between the orange node (V_1) and the green node. Thus, we have:

V_0=0 v

#### Final Answer: