Find V0 in the network in Fig. P3.12


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

Find V0 in the network in Fig. P3.12

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:

Find V0 in the network in Fig. P3.12

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.

I_1+I_2+I_3=0

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:

V_1=6 v

 

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=6 - 6

V_0=0 v

 

Final Answer:

V_0=0 v

 

This question can be found in Basic Engineering Circuit Analysis, 10th edition, chapter 3, question 3.12.

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