## USING NODAL ANALYSIS: INTERACTIVE EXAMPLE 3

In this section, the same problem is solved using nodal analysis. The applet presented below contains the default values. For the circuit in Fig. 38, you are required to obtain the impedance seen by the source, given the source voltage and the component values. The page containing the solution using the mesh analysis shows how the solution can be verified using the Tellegen's theorem and hence that part is not repeated here.

**SOLUTION:**

The circuit in Fig. 38 shows the unknown node voltages and the currents through the elements. The values of the source and the components are shown in the applet displayed below. You can edit the values for the impedances and the source, before clicking the **GO TO THE NEXT STEP** button. Note that the values for the source denote the peak values of the cosine and sine part of the source. The real part reflects the amplitude of the cosine function, and the imaginary part reflects the amplitude of the sinusoidal function. You need to click on the **GO TO THE NEXT STEP** button, to enable the second stage. When you click this button, data transfer to the next stage takes place.

You can form two node equations for the circuit shown in Fig. 38. The two KCL equations form a set of simultaneous equations. Let the first KCL equation be for node voltage **V**_{A}, and the second equation for node voltage **V**_{B}. Fill in the text fields of the second applet shown below. You can enter complex values into the boxes. For example you can enter values such as 1.5 + j2, -1. - j2, j3, 1, 2 + j etc.

You can ask the second applet displayed above to show the answers by clicking on the **Show Answers** button. Alternatively, you can enter your answers in the respective boxes and verify your answers.

Again you can verify your answers or have the answer shown to you. You gain nothing by asking the applet to display the answers. A help file has been provided to illustrate how this problem can be solved. You can click on the **HELP FILE **button shown below. A pop-up window opens showing the help page. While viewing the help file, keep this page open in order that the applets in the help file can access data from this page. You can close the pop-up window by clicking on the **Close PopUp Window** button.