# What is Nodal analysis: Definition + 176 Threads

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. ### Engineering Unable to model Transresistance amplifier with feedback correctly

I spent the whole day trying to figure why transresistance amplifier modelled with z-parameters does not match with nodal analysis results but I sill can't figure out. I desperate need help on this... I write down step by step what I did for a very simple transresistance amplifier here and hope...
2. ### Nodal Analysis and Two Dependent Current Sources

Hello, I came up with a circuit that has two independent voltage-controlled current sources. I want to calculate voltage gain: ##G_{U} = \frac{U_{2}}{U_{1}}##. Moreover, I want to practice the nodal method at the same time. Below I'm sending schematic with marked nodes V1, V2, V3 and V4. I...
3. ### Help with finding mesh currents and nodal analysis

Hi there, I have managed to work out the kirchoff's law bit but for the other two bits I just cant get started as I can get my head around it, its due in on monday I dont know why I left it so late!
4. ### Engineering Use voltage nodal analysis to solve for the current flowing in this AC circuit

Hi first time using this forum, I have some homework that I am entirely stuck on, can anyone help me with this question? I understand the placement of nodes, and that I need to convert complex numbers, but apart from that I have no idea what direction that I'm supposed to take in this. I don't...
5. ### Nodal analysis of this circuit with 2 sources and 4 resistors

Here is the question a. Plot nodes in the problem and indicate how many equations will be obtained. answer: two unknown variables b. Use node analysis. Derive the system of equations for the voltages in the circuit. question: Did I calculate right V_a and V_b? C. Calculate the...
6. ### Engineering Why Is Nodal Analysis Confusing in This Circuit Example?

Hello! Consider this circuit Now I am susposed to solve this using nodal analysis. The first step is to "prepare the network" so that I can set up the conductance matrix. Now I've tried it for a bit and was not really able to do it. So I went ahead and looked at the solutions and this is how...

8. ### Electric Circuit Analysis, Nodal Analysis and finding Voltage.

Summary:: The image shows two circuits, in the first one, using Nodal Analysis we find that V1=4.8V, but in the second circuit V1=10 because using KCL - 10+V1=0. I understand what happened in the first circuit, but I don't understand what happened in the second one, they look the same to me...
9. ### Engineering [Circuit Analysis] Am I on the right track with this problem?

*A is the node all the way to the left above the 30V but I didn’t end up using it because I don’t think you need it since the same as 30V, right? * I know I messed up somewhere because shouldn’t V1-4 = 30? After finding my V1 I used that value to find the other Vs and it ended up being close to...
10. ### Circuit problem with two sources and three resistors (Nodal Analysis)

Ans: 0.123A Tried mesh analysis and got it but didnt for nodal analysis

I have tried many times to solve this network, but can't understand how to get current in each resistors by superposition theorem. Please help me to solve and find currents in each 3 resistors with solution. Note:- The figure is attached below.

13. ### Using nodal analysis to solve for current

Hi all, Managed to get an answer out, but unfortunately, it doesn't correspond with the answer given ( –3.09 A) Would appreciate if one could check out what I did wrongly here: ## V_{1}=2\times 5=10V ## At node 2: ## \dfrac{V_{1}-V_{2}}{2}=12+\dfrac{V_{2}}{1}+\dfrac{V_{2}-V_{3}}{2}## We can...
14. ### Engineering Nodal Analysis of this Circuit using the Laplace Transform

Was just practicing some problems on the Fundamentals of Electric Circuits, and came across this question. I understand I will have to transform to the s domain circuit, which looks something like this: Then doing nodal analysis, I will get the following for the first segement (10/s-V1)/1 =...
15. ### Engineering Can this circuit be solved without nodal analysis?

help will be appreciated
16. ### Help with Circuit Nodal Analysis

Summary: Perform nodal analysis on a circuit to find voltages. For a laboratory I am trying to find the nodal voltages for a circuit we built using hand calculations. I have the answer as we ran the simulation which shows all the nodal voltages, however my nodal analysis seems to be wrong as I...
17. ### Solve Vo: Voltage Nodal Analysis w/ KCL Equation

I'm asked to solve for Vo for this equation. I've set the bottom node to be my reference node before applying nodal analysis. When included in the KCL equation for node at Vb, will the dependent voltage source 20iΔ be negative since the current through that element is leaving node C? Say, the...
18. ### Nodal Analysis Problem help (Double Supermesh)

That is, for Supernode -1,3 (12V branch) , we do Nodal Analysis and we have (V2-V3)/2 , over the 2 ohm branch. But this current is not included in the Equation 1 in the solution I have attached(Which is my only source to cross check answers/solution right now.) Is the solution wrong? Thanks...
19. ### Find the power supplied by the 1V source in the circuit using nodal analysis

My attempt: At node 1 > 4 = 6 + I1 Node 2 > I1 + I2 = I 2 Node 3 > 6 = I 3 + I 4 I1 = (V1 - 4)/21 In node 1, Using the equation for I1, V1 = -38V. I2 = (V1 - 4 - 1)/2 So, I2 = -21.5APower supplied by the 1V battery is P=VI P=-21.5 x 1 P=-21.5W I am not sure of my method, I just started...
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### What is ADPRES: An Open Source Nuclear Reactor Simulator?

Hello, My name is Muhammad Imron aka imronuke. I am interested in nuclear reactor computation and currently developing open reactor simulator called ADPRES which you can find in the my github repository. Regards,
21. ### Engineering Nodal analysis of an AC circuit

Homework Statement Hi I have this question as part of my assignment but cannot get my head around part b, I have worked out part a with an answer of -9.2+17.3i amps which from a previous thread I know is correct, but can't understand why the equations given in the previous thread are different...
22. ### Engineering Solve this Circuit using both Nodal Analysis and Mesh Analysis

Homework Statement [/B] Determine, Using the values given in TABLE A, the current I in the circuit of figure 2 by (a) Mesh analysis (b) Nodal analysis Circuit diagram and given variable attached. V1 = 120 V2 = j120 V3 = 14.142+j14.142 Z1= 2 Z2=-J5 Z3=4 Z4=-J5 Z5=J4Homework Equations [/B] KVL...
23. ### Find the current using Nodal Analysis

Homework Statement Find i using Nodal Analysis. Homework Equations V = I * R The Attempt at a Solution solve (1) , (2) , and (3) to find V1 , V2 ,and V3 V1 = 50/3 = 16.67 V V2 = 80/3 = 26.67 V V3 = 40 V 40 - 80/3 = 5i i = 2.667 A However , the correct answer is 1.522 A .. I don't know...
24. ### Confused about choosing current direction in nodal analysis

Homework Statement The problem states: Determine the voltage labeled v in the following circuit: https://ibb.co/hz0Q37 The variable is the voltage across the 2 ohm resistor. The ground I chose for this example is located in the center of the circuit. Homework Equations V=IR I guess. The...
25. ### Problem involving Source Transformation and Nodal Analysis

Homework Statement Homework EquationsThe Attempt at a Solution I have attempted and completed all questions. However, I am now trying part (b) with transforming the voltage source into a current source. I am unable to work out the current and I am unsure what to do next. I have included my...
26. ### Nodal analysis- Current directions for KCL

In node analysis, after labeling the nodes. I don't know how to choose currents direction to apply KCL. it seems too complicated.. and I end up every time getting different answers the the solution sheet. I've an exam tomorrow. would be much appreciated if you could help me better understand the...
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### What alternative methods can be used for solving nodal analysis equations?

Homework Statement Homework Equations using nodal analysis The Attempt at a Solution https://imgur.com/a/UNEDH the excel sheet is the matrix i set up then used cramer's rule. I think i got the method down but i just can't find the error so hopefully i overlooked something. The equation i...
28. ### Nodal Analysis with Dependent Voltage Source

Homework Statement Here is a diagram of the circuit and my redrawing with currents drawn: We are to find the power delivered by the dependent voltage source. I found a solution online, but I am not sure why they had the KCL line as:  \frac{v_1 - 160} {10} + \frac{v_1} {100} + \frac{v_1...
29. ### Using Nodal Analysis to determine current in a resistor

Homework Statement Homework Equations ##V = IR## ##\sum_{k = 0}^{n} I_k = 0## The Attempt at a Solution [/B] I set the bottom node as the reference node and worked from there to find the three equations for the loop. When I try to eliminate ##I_4## by using ##I_4 = I_2 - I_3## I run into...
30. ### Calculating Node Voltage using Nodal Analysis

1. Homework Statement The circuit is driven by a voltage source, Vs(t)= 8.2 cos(1.8 t − 0.25 )V . The circuit elements are given as follows. G1= 5 S,G2= 7.6 S,G3=3.8 S (Gi is the conductance of corresponding resistor Ri) L1= 20 H,C1= 5×10−2 F If we select Node 4 as the reference node...
31. ### How to solve a nodal analysis homework question?

Homework Statement This particular question has been raised in past posts and I have studied those posts but unable to take anything from them. Basically the question comprises 2 parts. Part A requires us to find the current through "I" using mesh analysis. By studying some of the posts on...
32. ### Engineering Find total power in a circuit with two power supplies

Homework Statement (a) Apply Nodal Analysis, writing down the equations which determine VA and VB, the voltages at nodes A and B [8] (b) Find values for VA and VB. [4] (c) By calculating the currents supplied by the 44 V and 2 V sources, or by any other means, calculate the total power...
33. ### Discovering Vc(0) using Nodal Analysis - Check out my Solution!

Homework Statement Find Vc(0) Homework Equations Nodal analysis The Attempt at a Solution
34. ### Solving for Vo: Nodal Analysis Approach

Homework Statement Determine the output voltage Vo(t) in terms of Vs Homework EquationsThe Attempt at a Solution If I were to use Nodal Analysis to solve this, would these be the proper nodal equations?\frac{V1}{-j1.6} + \frac{V1-Vs}{175} = 0 \frac{V_{I2}-Vo}{10k} + \frac{V_{I2}}{1k} = 0
35. ### Help with two electrical circuits please

Hey, I am having problems with this. I need help with these 2 circuits I am basically lost and not sure how to start. I need to find voltage, current and potency on each resistance help would be much appreciated, thank you http://imgur.com/trm1On0 http://imgur.com/a/KD3zr
36. ### Solving a Nodal Analysis: Find Va(t)

Homework Statement Find Va(t) using Nodal Analysis: Homework Equations Zc = 1/(jwC) Zl = jw*L The Attempt at a Solution W = 250 Z36mH = j9 ohm Z80mH = j20 ohm Z0.25mF = -j16 ohm (is capacitor impedance always negative? It says so in my instructor's notes but I forgot why) 20cos(250t) ->...
37. ### Nodal Analysis Help: Solving System of Equations

Homework Statement Attempted Solution: For my two nodal equations, I got: 40j + 20 - 12Va*j + 2Vb *j +4Va - 4Vb = 0 and 2Vb - 2Va - 6Vb*j - 4Va*j-10-20j Are these right? How do I solve this system of equations?
38. ### Mesh and nodal analysis don't quite match, but why?

Homework Statement [/B] Find I by mesh and nodal analysis Homework EquationsThe Attempt at a Solution ##V_{10}## is defined at the junction of ##Z_1##, ##Z_2## and ##Z_4##. ##V_{20}## is defined at the junction of ##Z_2##, ##Z_3## and ##Z_5##. ##0V## is defined at the junction of ##V_1##...
39. ### Engineering Nodal Analysis of a combo circuit

Homework Statement Attached is a image of the circuit that I am attempting to analyze:Homework Equations KCL The Attempt at a Solution So I know I should assign a place in the circuit where I should preform KCL after selecting a reference point. I selected the reference point as the 2ohm...
40. ### Exploring the Role of Batteries in Nodal Analysis

Homework Statement Homework EquationsThe Attempt at a Solution If I take KCL at node V1 (I'm assuming current traveling from nodeV2 to node V1) Current in = Current out V2 - 2volts / 2 ohms = V1 / 8 ohms so my question is, how does the battery (2 volts in this case) play a role in nodal...
41. ### Confused about solving RC circuits with nodal analysis

Problem is in the picture below. The problem is already solved, but I am confused as to why C(dv/dt) is positive and not negative, since the current is coming out of the capacitor and towards the point v(t), which is not away from v(t) like the solution shows. But if I solve the problem with...
42. ### The sign of the current and voltage

I was doing the following problem: And I was asked to find Iy. I found Iy to be 2.64 using KCL. However, the right answer was negative 2.64. Is it negative only because there is a dependant voltage source with "+ -" ? And why must it be negative? Does "-" in the final answer play a...
43. ### Nodal Analysis: Understanding KCL and Node Subtraction in Circuit Problems

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?
44. ### Find voltage using nodal analysis

Homework Statement Assignment: Find V_2 using Nodal Analysis Homework Equations 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...
45. ### Nodal analysis with dependent voltage source

Homework Statement In attached image. Just curious as to how their nodal analysis is correct. Homework Equations [/B] ##I_{in} = I_{out}## The Attempt at a Solution Solution in image. I am just not sure how they applied nodal analysis here to find that ##I_s = \frac{12}{12} +...
46. ### Nodal analysis with voltage source

Homework Statement Use nodal analysis to calculate Va, Vb, and the currents IE1 and IE2 without using source conversions I have tried this many, many times, and I must be missing somethingHomework Equations [/B] The equations I came up with: VA-10/ 1.1 + VA/1.2 +VA-VB/1.4 = 0 VB+2/1.5 +...
47. ### Nodal Analysis Problem: Where Did I Go Wrong in Using the Superposition Method?

Homework Statement The Attempt at a Solution [/B] At node B, ##i_s + 3 = i_2## ## 3 + 3 = i_2## ##i_2 = 6A## ##V_2 = i_2/R_2 = 3V## But, it seems that the answer is wrong. Using superposition method, the voltage is 4V Please tell me where I got wrong
48. ### Nodal analysis trying to find Voc

Homework Statement Find Voc Homework EquationsThe Attempt at a Solution This is what I have: (VA-9)/5 +VA/5 + 1.8 = 0 VA=0 -1.8 + VB/(60+10) +(VB-9)/20 VB=35 What I'm confused about is why you combine the 60 ohm and 10 ohm resistors for the VB nodal equation, but not the 25 ohm and 10 ohm...
49. ### Nodal Analysis: Solving Homework Problem

Homework Statement *Posted in the Screenshot* Homework Equations *Posted in the uploaded attachment* The Attempt at a Solution *Posted in the uploaded attachment*Hi all. Our lecturer gave us the question as part of an assignment but I'm not to sure if my approach and answer is correct. I...
50. ### Nodal Analysis Clarification - What are some conventions?

I've been assigned the following problem for homework in my Electrical Engineering class: *Note, the duplicate v2 is supposed to be v3. But I keep getting v1 = 4.10V v2 = 4.81V v3 = -1.19V and i0 = 52.9mA Every simulator I've put this into says it's wrong, yet I've attempted solving it...