Why is the Inducted Voltage Negative in Book B's Dot Convention?

In summary, the conversation discusses the dot convention in magnetically coupled circuits and the application of KVL in clockwise and counterclockwise directions. Both books mentioned are correct in their equations, and changing the signs on either side would not affect the overall result. The conversation also clarifies the correct placement of the dot and the direction of current in the equations. Ultimately, the correct equations are achieved in the end.
  • #1
degs2k4
74
0
Hello,

I have a doubt regarding dot convention in magnetically coupled circuits.

In book A, the following is stated:
152lrnr.png


But in book B, this is stated:
2uqhnib.png


In book B, why the inducted voltage of the second mesh (-j w M I1) has that negative sign ? According to dot convention, it is supposed that when the current enters into the dot, a positive inducted voltage appears in the dot of the second mesh right ?

Thanks!
 
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  • #2
Both books are correct. You seem to be concerned that the RHS of the questioned equation is negated, but what does it matter given that the LHS of said equation is zero! Change all the signs on both sides of the equation if you like, but it won't make any real difference.

BTW, that equation (2nd equation book B) comes from applying KVL in a clockwise direction around the secondary circuit. The equation that you seem to be expecting would come from applying KVL in a counter-clockwise direction, which ultimately would of course give the exact same equation.
 
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  • #3
uart said:
BTW, that equation (2nd equation book B) comes from applying KVL in a clockwise direction around the secondary circuit. The equation that you seem to be expecting would come from applying KVL in a counter-clockwise direction, which ultimately would of course give the exact same equation.

Thanks for your response.

OK, I think I understand it now... My idea about this is represented in the image below, is it correct?
moe1j.jpg


Just to check the last doubts, if the current of the second part were inverse, the equations would be ok like this?
25gvvom.jpg


And if the dot of the second part were at the bottom instead at the top...
dfe9s.jpg


Would this be correct ? (I am doubting whether I should change the sign of the rest of the equation or not, since the current direction has changed now)
 
  • #4
degs2k4 said:
Thanks for your response.

OK, I think I understand it now... My idea about this is represented in the image below, is it correct?
moe1j.jpg


Just to check the last doubts, if the current of the second part were inverse, the equations would be ok like this?
25gvvom.jpg


And if the dot of the second part were at the bottom instead at the top...
dfe9s.jpg


Would this be correct ? (I am doubting whether I should change the sign of the rest of the equation or not, since the current direction has changed now)

Nope, there's lot's of mistakes there. The sign of the "jwM" term is opposite to what it should be in all of the last three equations.
 
  • #5
uart said:
Nope, there's lot's of mistakes there. The sign of the "jwM" term is opposite to what it should be in all of the last three equations.

Thanks for your reply again. I was very confused, but I modified it again. Do you think it is correct now?

24nr811.jpg


And,
317io3d.png


Thanks in advance...
 
  • #6
Do you think it is correct now?
Yep, you've got it. :)
 
  • #7
Oh great! Thank you very much! :)
 

1. What is the Dot Convention Sign?

The Dot Convention Sign is a notation used in electrical engineering to represent the polarity of a transformer or inductor winding. It helps to determine the direction of current flow in a circuit.

2. How does the Dot Convention Sign work?

The Dot Convention Sign works by placing a dot at one end of a winding and a dot at the other end of the same winding. If the dots are on the same side, the winding has a positive polarity. If the dots are on opposite sides, the winding has a negative polarity.

3. Why is the Dot Convention Sign important?

The Dot Convention Sign is important because it helps to maintain consistency and avoid confusion when working with transformers and inductors. It also allows for easier analysis of circuit diagrams and calculations.

4. When should the Dot Convention Sign be used?

The Dot Convention Sign should be used whenever working with transformers or inductors, as it is a standard notation in electrical engineering. It is especially important in circuit analysis and designing new circuits.

5. Are there any exceptions to the Dot Convention Sign?

Yes, there are a few exceptions to the Dot Convention Sign. One exception is when the winding has more than two terminals. In this case, the dots may be placed on any two terminals, and the remaining terminals are assumed to be connected in series. Another exception is in certain special transformers, where the dots may be reversed due to different winding configurations.

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