Solving Network Nodal Voltages & Voltage-to-Current Conversion Tutorial

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SUMMARY

This discussion focuses on solving network nodal voltages and converting voltage sources to current sources using Norton's theorem. Participants clarify that a voltage source in series with a resistor can be transformed into a current source in parallel with the same resistor. The correct current value is derived using the formula I = V/Z, where V is the voltage and Z is the impedance. Additionally, the conversation touches on converting complex numbers from Cartesian to polar form, emphasizing the use of Euler's formula and phasor notation.

PREREQUISITES
  • Understanding of Norton's theorem for source transformation
  • Familiarity with complex impedance and phasor notation
  • Knowledge of Euler's formula for converting between Cartesian and polar forms
  • Basic proficiency in using trigonometric functions and calculators for angle conversion
NEXT STEPS
  • Study Norton's theorem and its applications in circuit analysis
  • Learn about complex impedance and how to perform source transformations
  • Explore phasor notation and its significance in AC circuit analysis
  • Practice converting complex numbers between Cartesian and polar forms using examples
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing and solving electrical networks will benefit from this discussion.

celect
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Can someone direct me to a tutorial for solving network
nodal voltages.
Also need to learn how to convert voltage source to a current source.
 
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a textbook should have everything you need..your in philly they must have a kick a*s Library there.. :smile:
 
Yea I was there today, will be back tomorrow.
 
celect said:
Can someone direct me to a tutorial for solving network
nodal voltages.
Also need to learn how to convert voltage source to a current source.
You cannot convert a voltage source into a current source. What you can do is to convert a voltage source in series with a resistor into a current source in parallel with the same resistor. This is Norton's theorem.
 
Ok I'm reading that chapter now, I attached a sample I'm working on now.
 

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    Sample1.GIF
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The solution you posted is wrong. The value of the current source is V/Z and what must be in parallel with the source is the series impedance, not the parallel you draw.
 
Regarding the right most circuit component, the symbol represents an inductor; yet the units is given in ohms.
 
inductor are coils , therefore i believe they can have resistance,
anyway,Checkout OpenCourseWare at MIT
 
So if I need to find E/Z = 20/9.9 = 2A

Now all I do is redraw circuit with 2A current source with
impedance parallel in circuit?
 
  • #10
If you want to do a source transformation on this circuit, you should probably look up phasors.
 
  • #11
celect said:
So if I need to find E/Z = 20/9.9 = 2A

Now all I do is redraw circuit with 2A current source with
impedance parallel in circuit?
No, you must make
I=\frac{20[cos(20)+jsin(20)]}{5.6+j8.2}
 
Last edited by a moderator:
  • #12
I'm confused on how to get proper result

I have now I = 20V <20 degree/ 5.6+J8.2
and I found in book the way to draw circuit.
but I don't understand how to use the equation with cos and j 20 sin.
 
  • #13
That's just Euler's formula and phasor notation:
"A-angle-theta" is phasor notation for A*ej*theta, which by Euler's formula is A[cos(theta) + j*sin(theta)], where A is a scalar value.
 
  • #14
You can also write 5.6 + j8.2 as 9.93 <55.67
So, I=\frac{20 &lt;20}{9.93 &lt;55.67}
That is an easiest form to evaluate the quocient.
 
  • #15
Here is a problem I got wrong, with the solution.
I don't understand how they got answer.


I don understand how you get
5.6 + j8.2 as 9.93 <55.67
how does 5.6 become 9.33
and j.2 = 55.67
 

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    1.GIF
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  • #16
celect said:
Here is a problem I got wrong, with the solution.
I don't understand how they got answer.


I don understand how you get
5.6 + j8.2 as 9.93 <55.67
how does 5.6 become 9.33
and j.2 = 55.67
I have transformed the complex number from its cartesian form to its polar form.
Z = x + jy = R<φ
Where R is the modulus of the complex:
R = \sqrt{x^2 + y^2}
and
\phi = tan^{-1}\frac{y}{x}
 
  • #17
Thanks its coming together now.

so my current = 20/9.93 = 2A

I don't understand how to get degrees yet
\phi = tan^{-1}\frac{y}{x}

do I take 8.3/5,5 tan and then use above formula?

what is the -1 how do i use on calculator?
 
  • #18
celect said:
Thanks its coming together now.

so my current = 20/9.93 = 2A

I don't understand how to get degrees yet
\phi = tan^{-1}\frac{y}{x}

do I take 8.3/5,5 tan and then use above formula?

what is the -1 how do i use on calculator?
tan^{-1} means arctan. It is the arc whose tangent is y/x.
And your current is I = 2 <-35.67.
When dividing complex numbers in the polar form you divide the moduli and subtract the phases.
 

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