# Node Voltage Analysis: Solving VA & VB

• kdeucesd
In summary, the speaker is struggling to determine the voltage at VA and VB in a circuit with VC and VD both at 10V. They mention using nodal analysis but are unsure how to set up an equation for VA due to a resistor and voltage source between it and the reference node. They have tried using nodal analysis and mesh current analysis but are seeking advice on how to solve the problem. They provide equations for VA, VB, and VC, and mention using 4 loop currents or simplifying the circuit to solve it.
kdeucesd
I am having a hard time trying to determine the voltage at VA and VB. I know that VC = VD = 10V. At first I thought this would be a simple setup, but I'm unsure about how to set up an equation for VA considering that there is a resistor and a voltage source between it and the reference node. I've built this circuit and made measurements with a DMM, I'm just trying to come to the same results using nodal analysis. Can anyone point me in the right direction?

#### Attachments

• Node.jpg
13 KB · Views: 444
For VA, I have (VA - 6)/100 + (VA - 10)/800 = 0
For VB, I have (VB - 10)/320 + VB/330 = 0
For VC, I have VC = 10

You could solve it by using 4 loop currents and then writing the KVL equations for the 4 loops.

Or you could start by simplifying the circuit, for example replace R3 and R5 by a single resistor ...

Using mesh current analysis was a breeze, but I am also asked to use node voltage.

As far as your second suggestion, I combined those resistors in the equations above.

Nodal analysis is a powerful tool for analyzing complex electrical circuits, but it can be challenging to set up equations for nodes that are not directly connected to the reference node. In this case, it sounds like VA and VB are not directly connected to the reference node, which can make it difficult to determine their voltages using nodal analysis.

One approach you could take is to use Kirchhoff's Voltage Law (KVL) to create a loop equation that includes VA and VB. This equation would include the voltage source and resistor between VA and the reference node, as well as any other components in the loop. You can then use the other known voltages (VC and VD) and the KVL equation to solve for the voltage at VA and VB.

Another approach is to use the concept of supernodes. A supernode is a combination of two or more nodes that are not connected by any elements, but have a voltage source between them. By treating these nodes as a single entity, you can simplify the circuit and create equations that include the voltage source and resistor between VA and VB. This can make it easier to solve for the voltages at these nodes.

It is also important to double check your circuit and measurements to ensure they are accurate. Sometimes discrepancies can occur due to faulty components or incorrect connections.

Overall, nodal analysis can be a complex process, but with careful consideration and the use of tools like KVL and supernodes, you can successfully determine the voltages at VA and VB. I hope this helps point you in the right direction.

## 1. What is node voltage analysis?

Node voltage analysis is a method used to analyze electric circuits to determine the voltage at each node or junction in the circuit. It is an important tool for understanding and designing electrical circuits.

## 2. How do you solve for VA and VB using node voltage analysis?

To solve for VA and VB, first, assign a reference node and label the other nodes. Then, write Kirchhoff's Current Law (KCL) equations for each node. These equations will have VA and VB as unknown variables. Finally, solve the equations simultaneously to find the values for VA and VB.

## 3. What is the purpose of using node voltage analysis?

The purpose of using node voltage analysis is to determine the voltage at each node in an electric circuit. This information is crucial for understanding the behavior of the circuit and can be used to calculate other important parameters such as current and power.

## 4. What are the advantages of using node voltage analysis over other methods?

Node voltage analysis is advantageous because it is based on Kirchhoff's laws, which are fundamental principles in circuit analysis. It is also a systematic and efficient method for solving circuits with multiple nodes and can handle both linear and nonlinear circuits.

## 5. Can node voltage analysis be used for all types of circuits?

Node voltage analysis can be used for any type of circuit, as long as it has multiple nodes and can be represented using Kirchhoff's laws. However, it may become more complex for circuits with a large number of nodes and may require the use of computer software for solving.

Replies
3
Views
1K
Replies
10
Views
2K
Replies
4
Views
1K
Replies
2
Views
910
Replies
1
Views
2K
Replies
68
Views
5K
Replies
38
Views
4K
Replies
5
Views
1K
Replies
5
Views
2K
Replies
2
Views
2K