How to Use Nodal Analysis to Find Voltages in a Circuit?

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Homework Help Overview

The discussion revolves around using the node-voltage method to determine the voltages v1 and v2 in a given electrical circuit, with specific current values provided. Participants are exploring the setup and equations related to nodal analysis.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to set up equations based on assigned nodes but questions the validity of their assignments and calculations. Some participants suggest reconsidering the necessity of a third node and explore the implications of assuming v2 equals v3. Others discuss the inclusion of resistors in the equations and how they affect the calculations.

Discussion Status

Participants are actively engaging with the problem, offering insights and alternative perspectives on the node assignments and equations. Some have provided revised equations based on their interpretations, leading to different voltage values. There is a recognition of the complexity involved in correctly applying the node-voltage method.

Contextual Notes

There is an indication of confusion regarding the connections of resistors and nodes, as well as the accuracy of initial calculations. Participants are navigating through these uncertainties while adhering to the constraints of the homework assignment.

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Homework Statement



Use the node-voltage method to find v1 in the circuit(Figure 1) if i1 = 6.2A and i2 = 1.5A .
Use the node-voltage method to find v2 in the circuit.

Figure_P04.8.jpg


Homework Equations



G = 1/R

QPFE3Hs.png


The Attempt at a Solution



Top side going from left to right, I assigned each node as 1, 3, then 2 (because of the way v_2 is assigned).

For Node 1, I had:
(v_1)/40 - (v_3)/8 = 6.2

Node 3:
-(v_1)/8 + (v_3)/80 = 0

Node 2:
(v_2)/120 = -1.5

Solving, I got v_1 = -5.06 V and v_2 = -180 V. These are wrong (obviously). Any assistance would be appreciated.

Moving image to bottom for visibility:

Figure_P04.8.jpg
 
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Hello G and welcome to PF. Clear story. Do you have a reason to assign node 3, or could you make do with just nodes 1 and 2 ?
Reason I ask is because V2 = V3 seems a reasonable assumption to me. (I will look up the thread where I made a complete fool of myself by completely missing such a thing -- fortunately others put me right...)

Found it -- don't laugh!
 
BvU said:
Hello G and welcome to PF. Clear story. Do you have a reason to assign node 3, or could you make do with just nodes 1 and 2 ?
Reason I ask is because V2 = V3 seems a reasonable assumption to me. (I will look up the thread where I made a complete fool of myself by completely missing such a thing -- fortunately others put me right...)

Found it -- don't laugh!

In that case where would I include the 80 Ohm resistor? Should it only be connected to v_2 on the equation?

If so,
Node 1:
6.2 = (v_1)/40 - (v_2)/8
-1.5 = (v_2)(1/80 + 1/120) - (v_1)/8

Solving, v_1 = 3.86 V and v_2 = -48.8 V. Which is still incorrect.

I'm out of attempts for solving for v_1, which I now know is 115 V.
 
Ah, I interpret the node a equation a little different: after all, the 8 ohm is also connected to node a !
 
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BvU said:
Ah, I interpret the node a equation a little different: after all, the 8 ohm is also connected to node a !

Ah, I see now. I didn't realize I had to include the resistors between each node as also connected to it individually.

1:
6.2 = v_1 * (1/40+1/8) - v_2 / 8

2:
-1.5 = v_2 * (1/80 + 1/120 + 1/8) - v_1 / 8

Ended with v_1 = 114.7 and v_2 = 88 (which is correct). Thanks.
 
Always nice to have the answer at hand... I was still plodding :smile:
And: you're welcome!
 

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