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

[degs2k4]

Hello,

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

In book A, the following is stated:

But in book B, this is stated:

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!

 

[uart]

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.

 

[degs2k4]

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?

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

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

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)

 

[uart]

Thanks for your response.

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

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

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

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.

 

[degs2k4]

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?

And,

Thanks in advance...

 

[uart]

Do you think it is correct now?

Yep, you've got it. :)

 

[degs2k4]

Oh great! Thank you very much! :)