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Suppose I connect an inductor to an ac source. Now a time varying current is produced and this causes change in magnetic flux linked with inductor coils and hence an induced is generated. But why this induced emf has to equal the applied emf? I have came across many resources stating Kirchoff law, but that does not help.

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  • $\begingroup$ Is this the sort of argument "that does not help"? $$\mathscr E_{source} - L \frac{dI}{dt} = IR,$$ so for $R=0$, $$\mathscr E_{source} = L \frac{dI}{dt}. $$ I ask so we can try and come up with another way of presenting the argument if necessary. $\endgroup$ Jan 6, 2020 at 22:12
  • $\begingroup$ @Philip wood you got it right. $\endgroup$
    – Sharad
    Jan 7, 2020 at 16:19
  • $\begingroup$ I've written an answer. I suspect that you won't like it! $\endgroup$ Jan 7, 2020 at 17:09

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$\mathscr E_{source}$, the work done per unit charge on charge passing through the source, is equal to $L \frac{dI}{dt}$, the work done per unit charge by charge going through the inductor (increasing the energy in its magnetic field). Why equal? Because, if $R=0$, there's nothing apart from the inductor and the source in the circuit for work to be done on or by!

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