Dot convention sign question

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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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Answers and Replies

  • #2
uart
Science Advisor
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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 wont 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
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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
uart
Science Advisor
2,776
9
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
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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
uart
Science Advisor
2,776
9
Do you think it is correct now?
Yep, you've got it. :)
 
  • #7
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Oh great! Thank you very much! :)
 

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