# Confusion about induced EMF and voltage in Ideal Transformer

When an IDEAL transformer primary is connected to an AC source, an EMF will be induced in the primary given by

$$E = N \dfrac{d(flux)}{dt}$$

And it must be given sign by Lenz's law. So it should be negative as for opposing the cause. So $E= - V$. But in some book it is given as $E= V$, so as to counter and exactly balance the cause.

But both are contradictory. I am getting very confused.

I have added the articles from both the books.

• Are you happy to accept that the induced emf (due to change in flux) is opposite to the sign of the applied voltage. It has to be this way or inductor action cannot be achieved and the universe will evapourate. Commented Mar 1, 2016 at 10:22
• @RobhercKV5ROB I am so sorry to use two -ve signs and create confusion. As it was not visible properly I used two -ve signs to make it visible. Please consider it as one -ve sign. Please now reconsider my question. Commented Mar 2, 2016 at 6:35
• Can you quote excepts from at least one book which uses each contradictory formula? I'm wondering if maybe the books are wording something slightly differently, which could make both books technically right, but incredibly confuskng if you don'r "catch it" on a minot description difference (which has messed me up before). For example, one could be describing back EMF during primary field building & one during primary field collapse (or any of about 6 other options). Commented Mar 2, 2016 at 12:27
• @RobhercKV5ROB I have added the articles from both the books. Please have a look. Commented Mar 2, 2016 at 14:27

There is no contradiction, only terrible wording by the second text book. Not to say the first book some shining beacon of clarity, but it's not as bad as the second book.

The second book says, "As per Lenz's law, the positive direction of this emf opposes the positive current direction...". Meaning, book 2's positive E1 is positive oppositional EMF. The first book decides to call this negative, and it is relative to V1. The second book just says it is equal in magnitude, but a positive value of an oppositional EMF is negative relative to the EMF it is opposing.

Clear as mud, right? It's a subtle difference in convention, but neither book is in disagreement. They both say the magnitude of E1 equals V1, and it does. And they both say E1 opposes V1, and it does. The sign doesn't matter, as depending on the convention you chose to use, other things will be signed or not such that it will ultimately still work out to the same answer.

This is not the only time you'll encounter something like this. Engineers, once they have become sufficiently experienced and grumpy, will often argue about which way current flows to pass the time. They will say that it clearly flows from - to + and everyone who disagrees is just wrong, or they will say the same thing only this time, current clearly flows from + to -. Is it the bubbles, or the water? In the end, it doesn't actually matter until you run out of things to argue about with other engineers, then it will matter a lot.

Just keep an eye out for things that are convention like this. Be sure to read the surrounding text carefully whenever there seems to be a contradiction. Usually it comes down to the author saying the same thing but from a slightly different perspective.

That said, current definitely goes from - to + and everyone who disagrees is wrong.

• Thanks a lot for your clarification. It made me understand the text better. :) Commented Mar 2, 2016 at 19:12
• This is pretty much exactly what I was expecting when I asked OP to post the articles for context. Unclear wording 1 + unclear wording 2 = total confusion 3... really easy to do if you're reading the textbooks to learn, since some particular textbook authors seem to think you should read their books only after you're already an expert in the matter. Commented Mar 2, 2016 at 19:21