Chapter 3, Problem 3.1HP

Use node voltage analysis to find the voltages $V_1$ and $V_2$ for the circuit of Figure P3.1.

To determine

The voltages $V_1$ and $V_2$ of the circuit using node voltage analysis.

Answer to Problem 3.1HP

The value of voltage $V_1$ is $4.8\text{V}$ and the value of voltage $V_2$ is $2.4\text{V}$ .

Explanation of Solution

Calculation:

The given diagram is shown in Figure 1

  

Apply KCL at the node $V_1$ in the above circuit.

  $\begin{array}{l}4-\frac{V_1}{3}-\frac{V_1-V_2}{1}=0\\ \frac{-4V_1+3V_2}{3}=-4\\ -4V_1+3V_2=-12\end{array}$   .......... (1)

Apply KCL at the node $V_2$ .

  $\begin{array}{l}\frac{V_2}{1+1}+\frac{V_2-V_1}{1}+\frac{V_2}{2}=0\\ V_2+V_2-V_1=0\\ 2V_2-V_1=0\\ V_1=2V_2\end{array}$   .......... (2)

Substitute $2V_2$ for $V_1$ in equation (1)

  $\begin{array}{l}-4\left(2V_2\right)+3V_2=-12\\ -8V_2+3V_2=-12\\ V_2=\frac{12}{5}\text{V}\\ V_2=\text{2}\text{.4}\text{V}\end{array}$

Substitute $\text{2}\text{.4}\text{V}$ for $V_2$ in equation (2).

  $\begin{array}{c}{V}_1=2\left(\text{2}\text{.4}\text{V}\right)\\ =4.8\text{V}\end{array}$

Conclusion:

Therefore, the value of voltage $V_1$ is $4.8\text{V}$ and the value of voltage $V_2$ is $2.4\text{V}$ .