# Mutual induction

How is the back induced current in the secondary coil transferred to the primary ? I know how mutual induction occurs (and I know that a the bst possible example would be a transformer) but I don't understand how it actually occurs ( I know it,but I still can't get it) I mean I get why when current flows in primary coil ( at the instant of switching the cicuit on) there is a change in current intensity by increase and that produces changing magnetic flux which in turn affects the secondary coil and an back induced current (or e.m.f) is formed in the secondary one. Then what ? How is this "induced current" transferred to the primary coil such that it opposes the original current (in the primary) and lets current grow slowly ? I should also mention that I'm not only under advanced level , but under ordinary level too , so please I beg you try to make the answer as simple as you could ,so that I won't be lost in a labyrinth of never-ending laws , eternal thanks in advance ~

Philip Wood
Gold Member

That is both a blessing and a curse. Many of us have it!

"I get why when current flows in primary coil ( at the instant of switching the cicuit on) there is a change in current intensity by increase and that produces changing magnetic flux which in turn affects the secondary coil and an back induced current (or e.m.f) is formed in the secondary one."

There is certainly an emf induced in the secondary coil, but there will only be a current in the secondary if the circuit is closed, perhaps by a resistor connected across the ends of the secondary coil.

In the primary coil there will be a back-emf induced due to the changing magnetic field that the primary itself sets up. This is self-induction.

If the secondary circuit is complete (i.e. there is a resistor or whatever connected across the coil) and a current flows, in the secondary, then this will itself produce flux in the core of the transformer, and this will induce another emf in the primary (or, if you prefer, change the emf induced in the primary). Obviously this is quite complicated. In a pre-university treatment of transformers what I've written about in this paragraph is usually not mentioned. I mentioned it only because it seemed to be what you needed to answer your question.

That is both a blessing and a curse. Many of us have it!

Sure is , in every possible subject I study !

"In the primary coil there will be a back-emf induced due to the changing magnetic field that the primary itself sets up. This is self-induction. "
The funny thing is , I asked my teacher if there is any self-induction during mutual-induction and he said what meant ' Yes , there is but we ignore it because we're only interested in the more important phenomenon '
If the secondary circuit is complete (i.e. there is a resistor or whatever connected across the coil) and a current flows, in the secondary, then this will itself produce flux in the core of the transformer, and this will induce another emf in the primary (or, if you prefer, change the emf induced in the primary). Obviously this is quite complicated. In a pre-university treatment of transformers what I've written about in this paragraph is usually not mentioned. I mentioned it only because it seemed to be what you needed to answer your question.
Yes , its exactly what I needed , thank you so much , but uhm , the obstacle lies within the whole visualization and Lenz law , for in the pic I've attached , if the primary coil (the one connected to the battery) induces emf in the secondary coil , the direction of the induced current will be opposite to the direction of original current in the primary coil , so the (I) induced will result in a magnetic flux around the secondary coil which will affect the primary coil and induce a current in a direction opposite to that in the secondary ! But wait a second ... isn't the current in primary coil already opposite in direction to the secondary ! and my ultimate problem arises here , please help and I'd be eternally grateful to you

Philip Wood
Gold Member
One or two things to get straight first of all.

• It's not currents (or flux) that are opposed, but changes in currents (or changes in flux).

• If current is flowing in the sense you've shown in your primary, then the flux in the core will be going from left to right. [You get this by a rule called the right hand screw rule (or right hand grip rule, or corkscrew rule)]. This means that if the core has ends (like yours) the right hand end will be North for the current as you've drawn it.

• The coils share a common core (which is usually a closed loop). It's misleading, I think, to have one part of the core magnetised in one direction, and the other part the other way.

• The current in a coil is given by the algebraic sum of the emfs in that coil's circuit, divided by the resistance in the circuit. The emfs may re-inforce or tend to cancel.

Now we can start work on your question. Let's call sense of current you've shown in your primary the positive sense.

If the primary current is positive and increasing (or negative but getting less negative), there will be an emf induced in the negative sense in the primary (self induction) and an emf induced in the negative sense in the secondary (mutual induction).

If the secondary has a resistor connected across it, a current will flow in the secondary in the negative sense. If this secondary current is getting more negative it will induce an emf in the positive sense in the secondary (self induction) and in the positive sense in the primary (mutual induction).

But be careful. Just because there is an emf in the negative sense induced in the secondary because the primary current is positive and increasing does't mean that the secondary emf is necessarily getting more negative; it might be getting more positive. This will depend on the way the primary current is changing with time, which will depend on the way the externally applied voltage changes with time.

If this all seems complicated - it is! Actually it gets simpler when you start to express it all mathematically.

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Philip Wood
Gold Member

sophiecentaur
Gold Member
2020 Award

It's a bit catch22, I know but there is no earthly reason why you can't learn some things 'off by heart' like the words of a silly song (which don't need any understanding - just learning).

When you were very young, you took things on board without demanding to understand them. You successfully use those (familiar but not understood) things as the basis for what you are now learning. So you are, in fact, capable of doing what you claim you cannot (you've been doing it all the way to your present state of knowledge).
Just allow yourself to do a bit more rote learning (a dirty word, these days, I know) and you should find that things will fall into place.

BTW, why are you expecting to understand the operation of a transformer if you are 'only' at what you call Ordinary Level? The basics of transformer theory only require you to have an idea about ratios of volts and numbers of turns. Beyond that, the subject is not Ordinary Level so don't be surprised if it's a bit too difficult to grasp 'in a vacuum'. The Laws of induction are introduced very slowly in School Physics because you will not have The Calculus to help you without A level Maths.

Yes, I have , thank you very much , I should tire you by one last request which is a mathematical application , please , that's help me consolidate the info in my head

It's a bit catch22, I know but there is no earthly reason why you can't learn some things 'off by heart' like the words of a silly song (which don't need any understanding - just learning).

When you were very young, you took things on board without demanding to understand them. You successfully use those (familiar but not understood) things as the basis for what you are now learning. So you are, in fact, capable of doing what you claim you cannot (you've been doing it all the way to your present state of knowledge).
Just allow yourself to do a bit more rote learning (a dirty word, these days, I know) and you should find that things will fall into place.

BTW, why are you expecting to understand the operation of a transformer if you are 'only' at what you call Ordinary Level? The basics of transformer theory only require you to have an idea about ratios of volts and numbers of turns. Beyond that, the subject is not Ordinary Level so don't be surprised if it's a bit too difficult to grasp 'in a vacuum'. The Laws of induction are introduced very slowly in School Physics because you will not have The Calculus to help you without A level Maths.

I know , but still I'd rather understand ,in addition , I kinda abhore maths ,specifically calculus,how can I achieve A.lvl if I can't even stand looking at it ? That's why I ask questions here, partly cuz I hate maths and parlty cuz my curriculum doesn't provide me with all the details needed to reach a comprehensive understanding of the subject, and of course I don't find people who can tolerate my questions and answer me accurately except here

Philip Wood
Gold Member
Is your algebra alright? I ask this, because, in my experience, it's unusual for a student with good algebra to hate calculus. If your algebra is good, I'm sure that, with the right book, you could make a new start on your calculus, and discover that it's alright after all.

sophiecentaur
Gold Member
2020 Award
I know , but still I'd rather understand ,in addition , I kinda abhore maths ,specifically calculus,how can I achieve A.lvl if I can't even stand looking at it ? That's why I ask questions here, partly cuz I hate maths and parlty cuz my curriculum doesn't provide me with all the details needed to reach a comprehensive understanding of the subject, and of course I don't find people who can tolerate my questions and answer me accurately except here

It's a shame you say you "hate maths". Maths is a language for communicating ideas and reasoning things out. Of course it will be a challenge but it is a necessary evil because you cannot do Physics just with arm waving.
I doubt that you would work out your finances (or the scores in your favourite sport) without using the appropriate maths.

One or two things to get straight first of all.

... • The current in a coil is given by the algebraic sum of the emfs in that coil's circuit, divided by the resistance in the circuit. The emfs may re-inforce or tend to cancel ...

I would say impedance, not resistance. If the load is inductive, like a motor, or solenoid, it has a reactance and a resistance, and the phasor sum of the 2 is impedance. Even with a pure resistive load, the xfmr secondary has a leakage reactance. This adds to the resistance in quadrature and the impedance is found. Not to nitpick, but V/I in the ac domain is Z, not R.

Claude

Is your algebra alright? I ask this, because, in my experience, it's unusual for a student with good algebra to hate calculus. If your algebra is good, I'm sure that, with the right book, you could make a new start on your calculus, and discover that it's alright after all.

Its ..... Okay I guess , hmm , I was hoping you could give me a problem to solve ,the ones I've solved are too simple , if there's no problem of course

To
It's a shame you say you "hate maths". Maths is a language for communicating ideas and reasoning things out. Of course it will be a challenge but it is a necessary evil because you cannot do Physics just with arm waving.
I doubt that you would work out your finances (or the scores in your favourite sport) without using the appropriate maths.

I don't want to sound like a baby who blames everyone for her mistakes but my teacher made me hate it by belittling me and such just because I understand thing slowly ,that really put me off the whole subject and what you say is true , its just that I came to see maths as a real tiresome bore which I could never be good at

I would say impedance, not resistance. If the load is inductive, like a motor, or solenoid, it has a reactance and a resistance, and the phasor sum of the 2 is impedance. Even with a pure resistive load, the xfmr secondary has a leakage reactance. This adds to the resistance in quadrature and the impedance is found. Not to nitpick, but V/I in the ac domain is Z, not R.

Claude
O.O I'm oblivious to all of this XD how is r = z and in what domain ?

sophiecentaur
Gold Member
2020 Award
To

I don't want to sound like a baby who blames everyone for her mistakes but my teacher made me hate it by belittling me and such just because I understand thing slowly ,that really put me off the whole subject and what you say is true , its just that I came to see maths as a real tiresome bore which I could never be good at

That's an even greater shame and your teacher may be at fault (perhaps he has a difficult group to deal with(?). Maths is a really useful tool and, if you are bothered enough to be using PF then you will find the motivation to get to 'love' Maths, eventually. One thing you can always bear in mind and that is that you cannot expect to know 'all' of Maths, ever. You do not need it. Everyone hits a wall with Maths but you can believe that, given enough time, you can make progress against one bit of that wall at a time and it will crumble for you. (Good feeling!!) Treat it as a tool and not as your life's work. It's far more nerdy than Physics so you don't want to go too far down that road LOL.

That's an even greater shame and your teacher may be at fault (perhaps he has a difficult group to deal with(?). Maths is a really useful tool and, if you are bothered enough to be using PF then you will find the motivation to get to 'love' Maths, eventually. One thing you can always bear in mind and that is that you cannot expect to know 'all' of Maths, ever. You do not need it. Everyone hits a wall with Maths but you can believe that, given enough time, you can make progress against one bit of that wall at a time and it will crumble for you. (Good feeling!!) Treat it as a tool and not as your life's work. It's far more nerdy than Physics so you don't want to go too far down that road LOL.

Yeah , maybe I could like it by getting to know and understand it , maths to me is more unlimited than physics XD I actually don't hate all of it tbh , I like limits and geometry before it became solid ;c; , maybe I'll give it a try next year (since I'm currently. Studying different subjects) and I don't mind going down that road too far XD I'm already loathed due to being introverted and a bookworm when it come to mythology and astronomy , I'd need some suggestions for books though c: