# Find voltage using nodal analysis

• Martin V.
In summary, the conversation was about solving for V_2 using nodal analysis. The method involved choosing a reference node, assigning node voltages, applying KCL to each non-reference node, solving the system of equations, and checking for errors. The final result for V_2 was found to be approximately 13.84V, with the correct equations for KCL being -I1 + I2 +I3 = 0 at node 1 and I4 = -I5 at node 2.
Martin V.

## Homework Statement

Assignment: Find V_2 using Nodal Analysis

KCL
U=R*I

## The Attempt at a Solution

- Chosen reference node
- Assigned node voltages
- Applied KCL to each non-reference node
- Solve system of equation
- Checked equations for obvious errors

See circuit drawing, node labels and assumed current direction in Nodal.png. Equation and solution of equation is to find in Nodal 2.png.

The right result should be that V_2=13,84V and not V_1 as I get.

#### Attachments

• Nodal.png
11.7 KB · Views: 539
• Nodal 2.png
5.8 KB · Views: 489
Not sure if this is the only mistake but KCL at node 2 is wrong...

Personally I prefer to write for my KCL equations to sum to zero so I would write...

Assume current leaving a node is +ve then..

+ I4 + I5 = 0
and
I4 = -I5

You might be tempted to skip steps but you have to be very fussy about the signs when applying KCL or KVL. I find I make fewer mistakes if I write my equation so it sums to zero and don't take shortcuts.

Martin V.
Your working for KCL at node 1 looks correct but I would write..

Assume current leaving the node is +ve..

-I1 + I2 +I3 = 0

Then rearrange it. It may seem fussy but by sticking to this version of the KCL definition I find I make few mistakes.

Martin V.
Both KCL-equations is wrong. With #2 is found the error in the equation around node 2. For node 1 were the 10 V battery not included in the equation. With the two change I get the correct answar - thanks! :)

#### Attachments

• Nodal 3.png
52.5 KB · Views: 541
I agree with Martin V. I found ##V_1\approx10.2426...(V)## and ##V_2\approx13.9012...(V)##.

## 1. How does nodal analysis work?

Nodal analysis is a method used to find voltage values at different nodes in an electrical circuit. It involves writing equations based on Kirchhoff's Current Law and solving them simultaneously to find the unknown voltages.

## 2. What are the steps to perform nodal analysis?

The steps to perform nodal analysis are as follows:
1. Identify all the nodes in the circuit
2. Select one node as the reference node
3. Write Kirchhoff's Current Law equations for each node (except the reference node)
4. Solve the equations simultaneously to find the unknown voltages

## 3. Can nodal analysis be used for both DC and AC circuits?

Yes, nodal analysis can be used for both DC and AC circuits. However, for AC circuits, the equations will involve complex numbers and phasors instead of real numbers.

## 4. What are the advantages of using nodal analysis?

Nodal analysis is a systematic and efficient method for finding voltage values in a circuit. It is more accurate than other methods like mesh analysis and can be used for circuits with any number of nodes. It also simplifies the process of solving complex circuits.

## 5. Are there any limitations of nodal analysis?

One limitation of nodal analysis is that it cannot be used for circuits with dependent sources. It also becomes more complex when there are a large number of nodes in the circuit. In such cases, other methods like mesh analysis may be more suitable.

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