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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?
Welcome to the PF.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?
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?
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.
Yes. Can you post an example circuit and show your reasoning now?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?
berkeman said:Yes. Can you post an example circuit and show your reasoning now?
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...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
Decoder said:(V1-0)/R2 + (V1-V2)/R3 - (B1-V1)/R1
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.
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.
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.
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.
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.
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.