Circuit problem with two sources and three resistors (Nodal Analysis)

In summary: Im pretty sure its wrong. Ill ask my prof to double check.In summary, a student attempted mesh analysis but did not get the correct answer. They tried converting from volts to amps and got 0.123A. After trying to get the answer using Thevenin's approach, they realized their mesh analysis was incorrect.
  • #1
wcjy
73
10
Homework Statement
Determine the current I (in Amperes) in the circuit below using nodal analysis.
Relevant Equations
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1614241575397.png

1614241653031.png

1614241662965.png


Ans: 0.123A
Tried mesh analysis and got it but didnt for nodal analysis
 
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  • #2
40I-V0? Subtracting a voltage from a current?
 
  • #3
haruspex said:
40I-V0? Subtracting a voltage from a current?
40I is from the current controlled voltage source. Isn't 40I in volts?
 
  • #4
haruspex said:
40I-V0? Subtracting a voltage from a current?
The rotated square (diamond) symbol with '+ -' is a controlled voltage source.
https://1.bp.blogspot.com/-VWAqITUrvhA/UY-k_NBxwfI/AAAAAAAAAUM/BPVlWJIFgXQ/s1600/sources.png

You can tell it's a voltage source because the '+ -' indicates polarity (as opposed to an arrow for a current source indicating current's direction).

'40I' indicates the output-voltage is numerically (in volts) 40 times the value of the current labelled 'I' (in amps) on the diagram.
 
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  • #5
wcjy said:
View attachment 278629

Ans: 0.123A
Tried mesh analysis and got it but didnt for nodal analysis
Can't see a problem. I also get I = 0.112(335)A and (for information) = 5.28(634) V. If you plug these values into check, you find that they give correctly balanced currents. Are you certain the answer should be 0.123A?

You could post your mesh analysis for checking. But purple on a black background is pretty eye-unfriendly and probably puts a lot of people off. (Typed-up using Latex is the preferred method.)
 
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  • #6
Steve4Physics said:
Can't see a problem. I also get I = 0.112(335)A and (for information) = 5.28(634) V. If you plug these values into check, you find that they give correctly balanced currents. Are you certain the answer should be 0.123A?

You could post your mesh analysis for checking. But purple on a black background is pretty eye-unfriendly and probably puts a lot of people off. (Typed-up using Latex is the preferred method.)
the system said the correct answer was 0.123. But anyways thanks, many people got 0.112 also. probably the answer is wrong. Gonna check with my professor.

My mesh analysis was wrong. I initially got 0.112 as well but i somehow tweak it to 0.123 thinking it was correct. Looking back, the change that i did, did not make any sense.

Anyways thanks so much for helping!
 
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  • #7
Steve4Physics said:
The rotated square (diamond) symbol with '+ -' is a controlled voltage source.
https://1.bp.blogspot.com/-VWAqITUrvhA/UY-k_NBxwfI/AAAAAAAAAUM/BPVlWJIFgXQ/s1600/sources.png

You can tell it's a voltage source because the '+ -' indicates polarity (as opposed to an arrow for a current source indicating current's direction).

'40I' indicates the output-voltage is numerically (in volts) 40 times the value of the current labelled 'I' (in amps) on the diagram.
Ok, I'd never come across that concept.
But the correct way to specify its value would be with units, namely, as 40IΩ.
 
  • #8
haruspex said:
40I-V0? Subtracting a voltage from a current?
Steve4Physics said:
You can tell it's a voltage source because the '+ -' indicates polarity (as opposed to an arrow for a current source indicating current's direction).
Yes. Also, it's in series with a resistor, which doesn't make a lot of sense for a current source.
 
  • #9
It's not nodal analysis, I prefer the source transformation (Thevenin) approach, but this is the answer. You get the erroneous solution by reversing the polarity of the dependent source [ (1+r/R2) ⇒ (1-r/R2) ].
20210225_130836.jpg
 
  • #10
haruspex said:
Ok, I'd never come across that concept.
But the correct way to specify its value would be with units, namely, as 40IΩ.
True, but by convention the units are usually omitted from the diagram and are assumed to be appropriate for the "conversion" implied by the sensed value and resulting output of the controlled source.

If units were specified on this diagram they would be more likely to take the form of Volts/Amp in order to indicate that so many volts are produced for a given current in amps, rather than being "reduced" from V/A to Ohms.

A similar convention occurs for the ##\beta ## value for transistors, where a simple apparently unitless value is given such as 200. In reality it represents the ratio of collector current to base current, the current amplification factor for the transistor, and so really should have units of Amps per Amp.
 
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  • #11
This is not something covered on the courses I teach but I was intrigued so decided to try to find out how to do such problems and have a go.
Perhaps not surprisingly, I can't get 0.123A as an answer. However, I'm wary of suggesting that's because the answer is wrong until I know for sure.

Please, @wcjy - it would be great if you could confirm one way or another when you ask your prof. Thanks :)
 
  • #12
rsk said:
This is not something covered on the courses I teach but I was intrigued so decided to try to find out how to do such problems and have a go.
Perhaps not surprisingly, I can't get 0.123A as an answer. However, I'm wary of suggesting that's because the answer is wrong until I know for sure.

Please, @wcjy - it would be great if you could confirm one way or another when you ask your prof. Thanks :)
yea the answer is wrong!
 
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FAQ: Circuit problem with two sources and three resistors (Nodal Analysis)

How do I determine the voltage at each node in a circuit with two sources and three resistors using nodal analysis?

To determine the voltage at each node using nodal analysis, you will need to follow these steps:

  • Identify the nodes in the circuit and label them with a unique number or letter.
  • Choose one node as the reference node and assign it a voltage of 0.
  • Write Kirchhoff's Current Law (KCL) equations for each of the remaining nodes, using the reference node as a reference point.
  • Substitute the values of the resistors and sources into the KCL equations.
  • Solve the resulting system of equations to find the voltage at each node.

What is the purpose of using nodal analysis in circuit problems?

Nodal analysis is a method used to analyze complex circuits and determine the voltage at each node. It allows for a systematic approach to solving circuit problems and can be used to analyze circuits with multiple sources and resistors. It is also useful in identifying the current flowing through each branch of a circuit.

Can nodal analysis be used to analyze circuits with more than two sources and three resistors?

Yes, nodal analysis can be used to analyze circuits with any number of sources and resistors. The number of equations needed to solve the circuit will depend on the number of nodes in the circuit. However, it may become more complex and time-consuming as the number of sources and resistors increases.

What are the limitations of nodal analysis?

Nodal analysis assumes that all the nodes in the circuit are connected by ideal wires, meaning that there is no voltage drop or resistance between nodes. This may not be the case in real-world circuits, which can affect the accuracy of the analysis. Additionally, nodal analysis can become more complicated and difficult to solve for circuits with a large number of nodes or non-linear elements.

Are there any alternative methods for solving circuit problems with two sources and three resistors?

Yes, there are other methods for solving circuit problems, such as mesh analysis and Thevenin's theorem. These methods may be more suitable for certain types of circuits or may be easier to apply in certain situations. It is important to understand the principles and applications of each method to determine which one is most appropriate for a given circuit problem.

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