Find V0 in the network in Fig. P3.12 using nodal analysis.
Image from: J. D. Irwin and R. M. Nelms, Basic engineering circuit analysis, 10th ed. Hoboken, NJ: John Wiley, 2011.
Solution:
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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: