Nodal Analysis: Understanding KCL and Node Subtraction in Circuit Problems

In summary: I see what you mean, it's easier to think of it like that and have them all as a sum and go from there. Thank you for the help you just saved my test grade tomorrow!
  • #1
Decoder
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While performing nodal analysis problems, I am always unsure of which node gets subtracted from during KCL. For example, if I have (V1-V2)/2k, how do I know that it shouldn't be (V2-V1)/2k?
 
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  • #2
Decoder said:
While performing nodal analysis problems, I am always unsure of which node gets subtracted from during KCL. For example, if I have (V1-V2)/2k, how do I know that it shouldn't be (V2-V1)/2k?
Welcome to the PF.

I use the convention that the sum of all currents *out* of each node is zero. That gives me the direction for each voltage subtraction. Makes sense?

EDIT -- to be a bit more clear. Since I'm summing the currents out of a particular node, the node's voltage is the first one in the subtraction equations for that node.
 
  • #3
berkeman said:
Welcome to the PF.

I use the convention that the sum of all currents *out* of each node is zero. That gives me the direction for each voltage subtraction. Makes sense?

Thanks, that makes sense. Say I have I1+I2-I3=0. How do you determine if I1=(V1-V2)/12k compared to I1=(V2-V1)/12k. Does it have something do to based on the reference node?
 
  • #4
berkeman said:
Welcome to the PF.

I use the convention that the sum of all currents *out* of each node is zero. That gives me the direction for each voltage subtraction. Makes sense?

EDIT -- to be a bit more clear. Since I'm summing the currents out of a particular node, the node's voltage is the first one in the subtraction equations for that node.

OH I think I understand it better now. So when I have the sum of currents equal to zero (KCL), the direction of the current determines which one is subtracted?
 
  • #5
Decoder said:
OH I think I understand it better now. So when I have the sum of currents equal to zero (KCL), the direction of the current determines which one is subtracted?
Yes. Can you post an example circuit and show your reasoning now? :smile:
 
  • #6
berkeman said:
Yes. Can you post an example circuit and show your reasoning now? :smile:

I can't figure out how to post a picture from my phone, but the way I'm doing it now is when the current goes through the resistor, I'm taking the node on the negative end and subtracting it from the node on the positive end of the resistor
 
  • #7
Decoder said:
I can't figure out how to post a picture from my phone, but the way I'm doing it now is when the current goes through the resistor, I'm taking the node on the negative end and subtracting it from the node on the positive end of the resistor
When summing the currents *out* of a node, subtract the far voltage from the near voltage (the near voltage is at your node). Don't worry what the values of the actual voltages are at this step. So ignore the current directions shown in the schematic below, and just write the two node equations for the sum of the currents out equals zero for each...

https://www.ibiblio.org/kuphaldt/electricCircuits/DC/00221.png
00221.png
 
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  • #8
So @ V1: I2+I3-I1=0
-> (V1-0)/R2 + (V1-V2)/R3 - (B1-V1)/R1

Would this be right?
 
  • #9
Decoder said:
(V1-0)/R2 + (V1-V2)/R3 - (B1-V1)/R1

Not quite. I would write it like this:

(V1-0)/R2 + (V1-V2)/R3 + (V1-B1)/R1 = 0

Remember to keep it in the form of the sum of all currents out of the node. When you start changing signs so it's not a sum anymore, it can be easy to get confused and make errors. :smile:
 
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  • #10
berkeman said:
Not quite. I would write it like this:

(V1-0)/R2 + (V1-V2)/R3 + (V1-B1)/R1 = 0

Remember to keep it in the forum of the sum of all currents out of the node. When you start changing signs so it's not a sum anymore, it can be easy to get confused and make errors. :smile:

I see what you mean, it's easier to think of it like that and have them all as a sum and go from there. Thank you for the help you just saved my test grade tomorrow!
 
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1. What is nodal analysis and how is it used in scientific research?

Nodal analysis is a mathematical and computational technique used to analyze complex networks, such as electrical circuits, fluid flow systems, and biological networks. It involves solving a system of linear equations to determine the voltage or pressure at each node (or point) in the network. This method is commonly used in scientific research to model and understand the behavior of complex systems.

2. Can nodal analysis be applied to non-linear systems?

Yes, nodal analysis can be used to analyze non-linear systems by using linear approximations or by applying numerical methods to solve the system of equations.

3. What are the advantages of using nodal analysis over other methods of network analysis?

Nodal analysis is advantageous because it allows for the analysis of complex systems with multiple inputs and outputs. It also provides a systematic and rigorous approach to solving network problems, and can be applied to both linear and non-linear systems.

4. Are there any limitations to nodal analysis?

One limitation of nodal analysis is that it assumes all components in the network are ideal and linear, which may not always be the case in real-world systems. Additionally, it can become computationally intensive for larger and more complex networks.

5. How is nodal analysis related to other network analysis techniques, such as mesh analysis?

Nodal analysis and mesh analysis are both methods used to analyze networks, but they differ in their approach. Nodal analysis is based on Kirchhoff's Current Law, while mesh analysis is based on Kirchhoff's Voltage Law. In nodal analysis, the unknown variables are the node voltages, whereas in mesh analysis, the unknown variables are the mesh currents. Both methods can be used to solve the same network, but nodal analysis is typically preferred for networks with multiple voltage sources, while mesh analysis is better suited for networks with multiple current sources.

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