Find V2 in Single Phase Transformer

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Discussion Overview

The discussion revolves around finding the secondary voltage (V2) in a single-phase transformer, with participants addressing a specific homework problem involving complex numbers and impedance calculations. The scope includes mathematical reasoning and technical explanations related to electrical engineering concepts.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem and equations but expresses difficulty with the calculation of current (I1) due to the presence of an imaginary number in the impedance.
  • Another participant suggests converting the impedance into polar form to facilitate multiplication and division of phasors.
  • There is a proposal to simplify the calculation by multiplying the numerator and denominator by the conjugate of the denominator to eliminate the imaginary unit from the denominator.
  • Participants discuss the implications of keeping the answer in complex form versus converting to polar form, with one participant seeking confirmation on the process of dividing complex numbers.
  • Clarifications are made regarding the ability to divide rectangular by polar forms, with mixed responses indicating uncertainty.
  • One participant notes that it is generally easier to convert to polar form for multiplication or division and to rectangular form for addition or subtraction.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the manipulation of complex numbers, with some agreeing on methods while others seek clarification. The discussion does not reach a consensus on the best approach to the problem.

Contextual Notes

Participants mention specific values and forms of complex numbers, but the discussion does not resolve the mathematical steps or assumptions involved in the calculations.

jsammut
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media%2F91c%2F91c7c515-c3ed-4661-8dfb-fcb78ae40a8a%2FphpA4NkXn.png
1. Homework Statement
Find V2. Everything else is available in the picture

Homework Equations


r1=r1+a^2*r2
x1=x1+a^2*r2
z2=a^2*r2
I1=vp/z2+r1+x1

The Attempt at a Solution


So I have used the first three formulas but it's the last one I am getting stuck on.
Since my x1 is an imaginary number how do I do this?
I'm currently stuck at I1=1200/192+4+j16
Can someone help me?

EDIT: VP=1200 NOT 1000 LIKE THE PICTURE STATES. EVERYTHING ELSE IS THE SAME
 
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jsammut said:
I'm currently stuck at I1=1200/192+4+j16
The impedance 192+4+j16 can be written as 196+j16.
Convert this into polar form. For multiplication and division of two phasors, you need their polar forms.
 
jsammut said:
I'm currently stuck at I1=1200/192+4+j16
You can also solve as:
I1 = 1200/(196 + j6). Multiply numerator and denominator by 196 - j6.
This will remove 'j' from denominator and then you can proceed.
j * j = -1.
 
Okay I got.
jaus tail said:
You can also solve as:
I1 = 1200/(196 + j6). Multiply numerator and denominator by 196 - j6.
This will remove 'j' from denominator and then you can proceed.
j * j = -1.

But then wouldn't I still have "j" in my numerator?
 
jsammut said:
Okay I got.But then wouldn't I still have "j" in my numerator?
Yes. If you want to keep the answer in complex form, you should keep it in the form
Ireal+jIreactive. Or you can simply convert it into polar form.
 
cnh1995 said:
Yes. If you want to keep the answer in complex form, you should keep it in the form
Ireal+jIreactive. Or you can simply convert it into polar form.

Okay. It's my first time working with Complex numbers. Just to confirm.
In order to do 1200/196+j16 I have to convert the numerator into polar form first. Reason for this is because 1200 is basically 1200∠0 which is polar form. You can not divide polar by rectangular.

Can you divide rectangular by polar?
 
jsammut said:
It's my first time working with Complex numbers. Just to confirm.
In order to do 1200/196+j16 I have to convert the numerator into polar form first. Reason for this is because 1200 is basically 1200∠0 which is polar form
Right.
jsammut said:
You can not divide polar by rectangular.

Can you divide rectangular by polar?
Yes and no.
 
T
cnh1995 said:
Right.

Yes and no.
Thank you, been a big help?
 
It's easier to convert into polar form when dividing or multiplying, and to convert to rectangular form when adding or subtracting. But if the denominator has simple terms like 1 + i or 1 - i then multiplying num and den by 1- i or 1 + i respectively is quicker than using calculator.
 

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