What is Nodal analysis: Definition and 176 Discussions

In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents.
In analyzing a circuit using Kirchhoff's circuit laws, one can either do nodal analysis using Kirchhoff's current law (KCL) or mesh analysis using Kirchhoff's voltage law (KVL). Nodal analysis writes an equation at each electrical node, requiring that the branch currents incident at a node must sum to zero. The branch currents are written in terms of the circuit node voltages. As a consequence, each branch constitutive relation must give current as a function of voltage; an admittance representation. For instance, for a resistor, Ibranch = Vbranch * G, where G (=1/R) is the admittance (conductance) of the resistor.
Nodal analysis is possible when all the circuit elements' branch constitutive relations have an admittance representation. Nodal analysis produces a compact set of equations for the network, which can be solved by hand if small, or can be quickly solved using linear algebra by computer. Because of the compact system of equations, many circuit simulation programs (e.g., SPICE) use nodal analysis as a basis. When elements do not have admittance representations, a more general extension of nodal analysis, modified nodal analysis, can be used.

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  1. J

    Solve Nodal Analysis Differential Equation for I1 with Reference Point under C

    Homework Statement Using nodal analisis we need obtain the differential equation 2. The attempt at a solution For I1 and take the point under C as reference, but i am stuck on it
  2. hdp12

    Engineering Solving a Circuit with Nodal Analysis

    Homework Statement I'm in a lab and we have this circuit & question as part of the pre-lab The Attempt at a Solution I began trying to use nodal analysis to get Va & Vb & to then use Vab to get the voltage and then the current but after doing what you can see above, I stopped because I...
  3. hdp12

    KCL Nodal Analysis & Power to Resistor (Need help)

    Homework Statement Here is the homework problem I was given: The Attempt at a Solution Above is the work that I began, however, I have an overwhelming feeling that I am incorrect and also I don't know how to continue to the next part/parts. Would someone please help me? Thank you H
  4. thegreengineer

    Nodal analysis, choosing reference node confusion

    I know that when we have to identify the nodes for solving a circuit with nodal analysis we always have to designate a reference node (which will be the ground node) as a reference for measuring the others' voltages. However I was practicing this and I found this example on...
  5. thegreengineer

    Nodal analysis, choosing number of nodes confusion

    Good evening people. Recently I started taking the "electric network analysis" course in my school. We already saw the mesh analysis method for solving circuits. Now we are seeing the node analysis method. I understand that the first step for this method is finding the number of nodes (and one...
  6. Bobby425

    Engineering Thevenin's equvalent circuit of the network?

    Homework Statement thevenin's equvalent circuit of the network Homework Equations thevenin's voltage thevenin's impedance The Attempt at a Solution using nodal analysis i tried to find thevenin voltage but the dependent source and the dependent variable troubling me!
  7. Bobby425

    How to find the voltage 'v' in the given network?

    Homework Statement Homework Equations [/B]The Attempt at a Solution
  8. J

    How Does Nodal Analysis Calculate Current in Complex Circuits?

    Homework Statement Determine using nodal analysis the current in branch Z4 Homework Equations [/B]The Attempt at a Solution [/B] Not sure how to handle the source v3 my solution so far has came up with answers that are not the same as the answers that I got for mesh analysis. Node A...
  9. J

    Steady State Sinusoidal using Nodal Analysis

    Homework Statement [/B] The photo included provides the problem but the professor stated that the right side source is supposed to be 100t and not 80t. The problem wasn't printed correctly in the book so I assume the solution wasn't either. The solution via the book is v1=2.56cos(100t+139.2°)...
  10. X

    Engineering Solving a weird circuit using nodal analysis?

    Homework Statement Homework Equations V=IR Kirchoffs Current Law The Attempt at a Solution I picked the middle node (the one surrounded by 3 resistors) as my reference. V1 and V2 are my other two nodes. I'm also assuming that V1>V2, V1<reference Using Kirchoffs Current Law: (Node 1)...
  11. G

    Find Maximum Power to Resistor R

    Homework Statement Homework Equations Pmax = ((VTh)2)/(4RTh) Rparallel = (R1R2)/(R1 + R2) KCL ΣI = 0 KVL ΣV = 0 The Attempt at a Solution Okay, so to find RTh, I remove all independent sources and set the "terminals" at R to have a 1A current running through them. Since there is a 30kΩ...
  12. P

    Mastering Nodal Analysis for KCL and Ohm's Law: Solving Branching Node Equations

    hello! I have some difficulty in nodal analysis I want to know basically how to apply KCL and Ohm's Law to find the equations few branches meet in a node I know that KCL means that sum of currents that enter are equal to the sum of currents are leaving the node the problem is that I may not...
  13. G

    Superposition Principle to Solve Circuit

    Homework Statement Homework Equations KVL: ΣV = 0 KCL: ΣI = 0 v = iR The Attempt at a Solution I started by removing the independent current source to leave an open circuit. Then I attempted nodal analysis at nodes v1, v2, and v3: KCL @ v1: (v1 - v2)/10 = v1/40 KCL @ v2: (v2 - v1)/10 -...
  14. Feodalherren

    Engineering Nodal analysis of a fairly simple circuit

    Homework Statement Given this circuit, find i. Homework Equations Nodal analysis, Ohm's law other basic EE equations. The Attempt at a Solution The stuff in blue is given in the problem. The red is my attempt at a solution. So first off a general question that I have is, when I'm doing...
  15. G

    Finding Voltages in a Circuit with Nodal Analysis

    Homework Statement Homework Equations KCL: Σi = 0 KVL: Σv = 0 The Attempt at a Solution Using KCL: 15 = (v1)/8 + (v2)/4 Using KVL: (v1) - (v2) = (I2)R + 10 (v1) - (v2) = (I2)2 + 10 (I2) = (v1)/8 (v1) - (v2) = (2)((v1)/8) + 10 (v1) - (v2) = (v1)/4 + 10 Now there are two variables and...
  16. Q

    Engineering Nodal analysis question -- circuit analysis

    Homework Statement We have the circuit in the figure.I have to find the current i using nodal analysis Homework Equations 1/6 F =-3j 1/2 F= -j 1/2 H= j The Attempt at a Solution So we have the equations Node V1 : [(7-V1)/(4-3j) ]=[ V1/3 ]+ [(V1-V)/-j] Node V : [(V1-V)/-j] =(V )+ (V/j) In...
  17. H

    Engineering AC circuit analysis -- mesh and nodal

    Homework Statement Determine, using the values given in TABLE A, the current I in the circuit of FIGURE 2 by: (a) mesh analysis (b) nodal analysis. Any help verify for part (a)? And to help me get started with (b) as V3 is driving me nuts. Homework EquationsThe Attempt at a Solution For (a)...
  18. M

    Mastering Mesh and Nodal Analysis with KVL for Complex Circuits

    Homework Statement Please see a picture Homework Equations KVL The Attempt at a Solution V1-I1Z1-(I1-I2)Z4=0 Z2(I2-I4)+Z5(I2-I3)-(I2-I1)Z4=0 Z3I3+V2+Z5(I3-I2)=0 V3+Z2(I2-I4)=0 Any clues are appreciated..
  19. Q

    Nodal analysis exercise,are my equations correct?

    Homework Statement We have the circuit in the figure.I have to find v using nodal analysis only. Homework Equations Converted 1/6 F to -3j and 2sin2t to -2j. The Attempt at a Solution In node v1 we have the equation 6= -12+ [v1/2] + [( v1-v)/1] In node v we have the equation 2j+ [(v1-v)/1]=...
  20. C

    Direction of Current between nodes

    Say for example you had the following circuit. Since it is hard to determine which source will have a bigger influence on current I am unsure of how I would determine which way the current would flow between each node.
  21. _N3WTON_

    Solving Circuits: A Nodal Analysis Approach

    Homework Statement Answer the following questions about the given circuit. These questions will walk you through the steps of the analysis process we call nodal analysis, which is applicable to all electric circuits. 2.1 (3 pts) A quick Fermi-type problem before we start. Use Ohm’s Law to...
  22. V

    Resistive Network. - nodal analysis

    Homework Statement http://learn.lboro.ac.uk/file.php/1844/Quiz_figures/Chins_Files/Q11.jpg In the above circuit V1=17 Volts V2=8.5 Volts V3=4.25 Volts I1= 4 Amps I2= 5 Amps R1=4.25 Ohms R3=6.375 Ohms R4=1.0625 Ohms R5=2.125 Ohms R6=2.125 Ohms Calculate the following: a) Magnitude of...
  23. C

    Use the Node Voltage method to solve

    Homework Statement From the above circuit find VCB and VDG Know Data: VE = 0 (ground) Homework Equations KCL and Ohm's Law are used in Node Voltage Method. The Attempt at a Solution I decided I would determine the node voltages then work out VCB and VDG afterwards. 1. KCL and Ohm's law at...
  24. 159753x

    Easy electrical engineering question - why is my answer wrong?

    Hi! This is simple mesh analysis. I wanted to try to solve the problem with nodal analysis. 1. Homework Statement Homework Equations V = IR We are supposed to use mesh analysis or node analysis. The Attempt at a Solution [/B] First step: the two current sources (independent and...
  25. STEMucator

    Solving Voltage Source Nodal Analysis: Find Vo

    Homework Statement Use nodal analysis to find ##V_o##. Homework Equations ##\sum I = 0## ##I = V/R## The Attempt at a Solution So the book started throwing voltage sources into nodal analysis and I'm a bit unsure about this problem. The answer is listed as ##V_o = 3.89 V##. All they...
  26. R

    Confusion with Nodal Analysis w/ Sources

    Hi , I'm currently stuck on a problem that requires to be solved with nodal analysis. I'm confused to what signs should I use when there's a voltage source in the loop. The problem: I already know the answer from the solutions but what I found is at V_0 : (V0 - 60V)/12 + V0/12 + (V0...
  27. W

    How do I solve a Nodal Analysis problem with multiple unknowns?

    Hi, V1 for this problem is 400mA and no matter how I work this problem I cannot get the correct answer. V2=V1+6 For the second equation, I don't know what to do with 14V. I've tried subtracting it from V1 divided by the 4 ohm resister, most logical, and that doesn't work. I've tried multiple...
  28. W

    Problem With Nodal Analysis Question

    Homework Statement https://courses.edx.org/static/content-mit-802x~2013_Spring/html/ps3_p3_fig1_a.png $$ R_1 = 7 \Omega \quad R_2 = 49 \Omega \quad R_3 = 52 \Omega \quad R_4 = 91 \Omega \quad R_5 = 101 \Omega $$ $$ V_1 = 5V \quad V_2 = 39V \quad V_3 = 44V$$ Homework Equations $$ I =...
  29. gfd43tg

    Can Supernode Analysis Solve Your Circuit Analysis Problems?

    Hello, I am having some difficulty solving this problem and I have doubts regarding my expression with the supernode. Basically, I said that current is negative if the current in my first KCL equation in the first term V1 - vs / ZL1 Here is my attempt And here is a photo to part B that I will...
  30. H

    Nodal Analysis: Imaginary Numbers

    Homework Statement I have to find the Thevinin Equivalent for the following circuit. I am assuming the current is going out of the node. V= node between inductor and capacitor V0 = V[40/(40-150j)] (V-75)/(600+150j) + (-0.02V0) + V/(40-150j) = 0 The only problem I have is with the last...
  31. M

    Engineering Two EE questions - nodal analysis and circuit modeling

    Two EE questions -- nodal analysis and circuit modeling Homework Statement Homework Equations I was given R1, R2, and Iα(t), the time for the switch to closed (50μs<=t<=100μs) The question is asking about the energy associated with 2 sources and dissipated in R1, R2.The Attempt at a...
  32. gfd43tg

    Engineering Nodal Analysis with AC circuit

    Homework Statement Apply nodal analysis in the phasor domain to determine ix(t) in the circuit below. Homework Equations The Attempt at a Solution This is super confusing to calculate in the phasor domain, I was just wondering if anyone could check my calculations and see if they...
  33. Gliese123

    Engineering The current in a circuit using nodal analysis

    Homework Statement Hi! "Write an equation for I1." Here is the circuit: That is the question. I suppose one could do this many ways but I've decided to do it with nodal analysis. The problem here is that we only got an ideal current source. I have actually no clue. So, I'd try to...
  34. gfd43tg

    Engineering Struggling with Nodal Analysis and Voltage Calculations

    I am having a little issue with this problem, because when I do nodal analysis, I get the voltage of the node above the 5 kΩ resistor to be nearly 15 V. I am assuming all of the capacitors are saturated, and therefore act as open circuits. That means no current goes through the 20k or 30k...
  35. M

    Simple Nodal Analysis Problem Solution and Explanation

    Homework Statement Homework Equations KVL and KCL The Attempt at a Solution Let V = V1 and the Voltage across the 2 ohm resistor be V2 just for reference. Step 1: KCL @ Supernode: V1/3 + V2/2 + 21/4 + V3/6 = 0 I think my problem is here somewhere. Does V3 = V2 because...
  36. C

    Nodal Analysis for Energy Stored

    Homework Statement The temperature response of a fin is to be approximated using the finite difference method. The fin is 3 cm long and has a square cross-section that is 5 mm on a side. The fin is aluminum, with thermal properties ρ=2700 kg/m3, k=200 W/(m-K), and c=900 J/(kg-K). The fin...
  37. I

    How do I solve nodal analysis with a 2Ix voltage source at the red node?

    How do I find the voltage at the node with the red dot using nodal analysis? The 2Ix voltage source to the left of the node with the red dot makes it confusing for me... Thanks
  38. P

    Nodal analysis voltage confusion

    So the voltage across the R2 resistor is given as vT-0 = vT But then the voltage across the R1 resistor is given as "vT-Vs1" I'm not sure which two nodes the voltage across R2 involves. Is it the same as R1? Also, I am not sure of the voltage source vs1. Across which two points does it apply?
  39. I

    Nodal Analysis: Understanding Method & Solving for Unknown Voltage

    I understand their method. However, if you use the node to the left of the 2 ohm resistor (the node where the voltage = 75 V) then you get: (75-Vx)/2 -10 = 0 so 75-Vx = 20 so Vx - 75 = -20 Vx = 55 V But this is not 25 V as it should be? When doing nodal analysis, do you have to...
  40. I

    AC Circuit with possibly nodal analysis

    Homework Statement Homework Equations impedance equations for capacitors and inductors The Attempt at a Solution I thought something like that might do and then just do a matrix and solve for Va, but I am having second thoughts seems like I am over doing it.
  41. F

    Nodal analysis of simple hydraulic system

    Hi, I'm trying to model a simple hydraulic system using python programming language and have difficulty with math. It's basically 3 tanks interconnected with pipes (see attached picture). Tanks are filled with some kind of fluid and are under different pressures (initial pressures P1, P2...
  42. bibo_dvd

    Nodal Analysis , Can't Understand the direction of a current

    Nodal Analysis , Can't Understand the direction of a current ! In This Question "Nodal Analysis" we will apply kirchhoffs current law .. My Question is : Why in Fig 8.51 and 8.52 the currents take these directions ?? i tried to get it but i couldn't Photos : Thanks...
  43. R

    Confused on Voltage Calculations: Using Nodal Analysis to Find Input to Amp

    I have attachted the question as a picture: my first attempt i calculated the voltage through the auxillary circuit to be 10V but i am confused of where the 0.5 A plays in this part, then i used nodal analysis to find the voltage input to the amplifier but up to that point i am confused of...
  44. S

    Nodal Analysis problem with voltage sources

    Homework Statement I have a circuit and I need to find the Nodal Equations that would mathematically describe the circuit, then proceed to finding the voltages at each node using Cramers rule and the currents at nodes 2 and 4. I don't think I would have much of a problem utilising Cramers...
  45. U

    Nodal Analysis- direction of currents flow

    The figure shows a transistor with a bias circuit. If Ic=50IB and if VBE=0.7V, find VCE. My question is: The current through 700Ω resistor is H=[0.7+(51IB(250))]/700, then when KCL is applied at the left hand node, the current flowing through the 3kΩ resistor suppose to be (according to...
  46. E

    Nodal Analysis Help, 1 equation 2 unknowns

    1. 2. V=IR, Nodal analysis 3. Based on where I have drawn my ground, V2=-10V, V1=3I. From this I should just have 1 equation with 1 unknown (if I have done this correct). My KCL equation for node V1 is (V3+10)/8 + (V3-3I)/2 + V3/12. I am stuck, I need to find an equation for I in...
  47. X

    How to Solve Circuit Nodal Analysis for Vx?

    Homework Statement Find Vx. Homework Equations KCL V=IR The Attempt at a Solution First since the undrawn voltage source is in parallel with the 2 ohms resistor. Therefore, I concluded that the voltage source is also -3V For node labeled V1: Iin-(-3V/2ohms)+I from V3 to V1=0...
  48. E

    Nodal Analysis 1 equation 2 Unknowns Problem

    http://imgur.com/W9sWTv7V=IR, that is all I think 3. I have put my ground at the bottom branch. I have tried to write a KCL for the top branch but end up with 0=0 when I substitute in equivalencies. My KCL: (V1+5Ix-0)/20+2+Ix=0. (V1+5Ix)/20=-2-Ix. So 0=0. I am not sure if I am writing my KCL...
  49. C

    Nodal Analysis of a Voltage Dependant voltage source, no pretty answer

    Homework Statement five branches left most branch: 50 Volt source second left most: 10 ohm resistor shared branch between the second left most branch and center: 10 ohms (Voltage drop from left to right= V delta) center branch: 30 ohm resistor between center and second right...
  50. A

    REAL QUICK HELP nodal analysis?

    REAL QUICK HELP nodal analysis?? Homework Statement Homework Equations n/aThe Attempt at a Solution i am having trouble with my nodal equations for nodes 1 and 3. and that's just for the current on the top of those nodes, where the 4V is at. For node 1 my current equation is (V1-4)/0.2 for the...
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