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Consider a voltage source V connected to a coil. By Faraday's Law e=-(dƛ/dt). I don't understand the direction of the induced voltage e making v=-e

However, if we treat the coil as a circuit element and use Kirchoff's law, v-e=0(since v is seen as a voltage drop) so v=e

Can someone explain what am I missing out on between the two(more specifically Faraday's laws).

Nigel Goveas
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  • The minus sign is only there to indicate that the induced emf opposes a change of current. Place the + and - signs on the inductor to oppose the assumed positive current direction. – Chu Nov 18 '19 at 12:09

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The answer involves vectorial form of KVL from Electromagnetics and the fact that time-varying electric field around a loop formed is non-conservative and hence line integral of electric field intensity which is by definition voltage, is not path independent and not 0 for a closed path, and thus KVL, in its unchanged form, won't hold true...but to hold very useful, KVL still valid, 'mathematical adjustments' were made. This maybe little hard to understand at beginning especially if one is not well versed with electromagnetics theory.

But without going into complex mathematics, I prefer to look at things this way : Induced emf is by definition, +ve in the direction as given by right hand thumb rule is ( - L di/dt).

But if you consider inductor as passive circuit element, then it is nothing more than a mathematical adjustment (so that KVL would be applicable in its very well known form) to set voltage drop across it as +L di/dt, the terminal at which current enters being taken positive.

To give simple illustrating example : In a ckt having just an inductor supplied by 1-phase voltage supply, Induced emf (whose definition states that it is in direction given by right hand thumb rule) in an inductor is 180 degrees out of phase from conventional voltage drop across the inductor, taken positive in the direction of current. I will add figures when I get time. But a look here might be worth : MIT Notes on inductance

PS : This is personally my favorite question (and I'd like to add alot to it later) perhaps because it bugged me until I completed my graduation, but I admit a good answer would involve concerned electromagnetic theory as well.

Deep
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  • Hi! I finally understood the direction of the induced voltage for a single cool(self inductance) with the help of that pdf you posted. Now I want to know how induced emf is for mutual inductance. If you have any pdf or some material do send it my way – Nigel Goveas Nov 19 '19 at 17:48
  • @nigel goveas that's the pdf fron MIT, it looks this is the one which discusses mutual inductance too, in fact that's the very first topic. But you can always Google around typing topic name followed by 'MIT' and you'll more than not always find quality stuff. And yeah you can accept answer by clicking on ☑️ if you wanted to. – Deep Nov 19 '19 at 17:56