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I'm a little confused.. When I write the equation of the circuit, do I have to keep the signs of the induced emf and self-inductance opposite?

I'll try to explain better my doubt: Consider a coil that has resistance R and inductance L. Running a current will give rise to both an induced emf and self-inductance, and the situation is:

induced emf= -k

self-inductance= $-L \frac{dI}{dt}$

Now, my question is: the equation of the circuit is given by:

$-k -L \frac{dI}{dt}=RI$

or by

$k -L \frac{dI}{dt}=RI$ ?

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  • $\begingroup$ Refer to Lenz's Law: Induced current has a direction such that its magnetic field opposes the change in magnetic field induced in the current. $\endgroup$
    – signus
    Sep 24, 2013 at 20:06
  • $\begingroup$ @Signus and so..? $\endgroup$
    – sunrise
    Sep 24, 2013 at 20:07
  • $\begingroup$ @Signus I think that the correct expression is the second, because the self inducted emf opposes to the inducted emf.. do you agree? $\endgroup$
    – sunrise
    Sep 24, 2013 at 20:12
  • $\begingroup$ I do believe the second equation is correct as the self-inductance does oppose the induced current already on the wire/coil. That is why I mentioned Lenz's Law. I always think to myself "induction is always in the opposite direction of what my brain thinks." $\endgroup$
    – signus
    Sep 24, 2013 at 20:25
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    $\begingroup$ Doesn't the term $-LdI/dt$ already account for the induced EMF $E$ so there must be only one of these in the equation? $\endgroup$ Sep 25, 2013 at 1:25

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