Find V1 and V2 in the circuit


Find V1 and V2 in the circuit in Fig. P3.5 using nodal analysis.

Find V1 and V2 in the circuit

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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We will label two nodes to perform nodal analysis on this circuit as follows:

Find V1 and V2 in the circuit

Let us first look at node V_1, the orange node.

We can write a KCL expression like so (note that k=10^3 and m=10^{-3}):

I_1+I_2+6m=4m

(remember that while I_1, I_2 and the 6mA leave the node, 4mA is coming into the node)

We can express these currents in terms of voltage and resistance using (I=V/R).

\dfrac{V_1}{6k}+\dfrac{V_1-V_2}{4k}+6m=4m\,\,\,\color{orange} {\text{(eq.1)}}

 

Let us now look at node V_2, the purple node and write a KCL expression.

I_3+I_4+I_5=6m

Again, expressing these currents in terms of voltage and resistance, we get:

\dfrac{V_2-V_1}{4k}+\dfrac{V_2}{6k}+\dfrac{V_2}{3k}=6m\,\,\,\color{purple} {\text{(eq.2)}}

 

Solving equations 1 and 2 simultaneously gives us (see full steps):

V_1=0 v

V_2=8 v

 

Final Answer:

V_1=0 v

V_2=8 v

 

This question can be found in Basic Engineering Circuit Analysis, 10th edition, chapter 3, question 3.5.

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