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I guess this has been asked before many a times. But I searched for it and couldn't find the question. Any kind of qualitative answer will be really helpful.

When a magnetically charged inductor is connected in series with a resistor, it is known that the current decays exponentially through the resistor and becomes zero after a long time.

This is also mathematically supported by the equation, $i(t)=I_{o}e^{\frac {-tR}{L}}$. My question is how can current decrease to zero ? How can charges flowing in the circuit decrease to zero ?

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Heat energy

If your question is ‘where’ the current (essentially the EMF) stored in the inductor goes, it would be lost as heat energy when the current passes through the resistor.

Since current requires the electron to move, when they lose their kinetic energy as heat, the current becomes zero.

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  • $\begingroup$ Can electrons come to rest in a closed circuit ? $\endgroup$
    – User12121
    Commented Sep 10, 2021 at 16:05
  • $\begingroup$ @User12121 when we talk about current, we mean net flow of electrons. When a potential difference is applied across a conductor, there is net flow from the higher potential to the lower potential. Electrons aren’t necessarily as rest when there is no current, they posses thermal kinetic energy. However, this motion is random and the net result being the electrons ‘cancel’ each others motion on a large scale, meaning no net movement of electrons meaning no current. $\endgroup$
    – m-Xylene
    Commented Sep 10, 2021 at 16:11
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    $\begingroup$ that makes sense. Thanks for the explanation ! $\endgroup$
    – User12121
    Commented Sep 10, 2021 at 17:04
  • $\begingroup$ Since the current in an active inductor is zero (constant), the potential difference across it is zero. What then provides the potential difference across the resistor for the flow of current? @m-Xylene $\endgroup$
    – KPS
    Commented May 27 at 19:51
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My question is how can current decrease to zero ? How can charges flowing in the circuit decrease to zero ?

The current decreases to zero because all the energy initially stored in the magnetic field of the inductor is dissipated as heat in the resistor. The charges in the circuit don't decrease to zero, they simply stop moving in the form of current.

Hope this helps.

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  • $\begingroup$ Hmm !!! I had a kind of strange notion that electrons' motion can/will never be stopped in a closed circuit, because they are continuously moving in a conductor. $\endgroup$
    – User12121
    Commented Sep 10, 2021 at 16:04
  • $\begingroup$ @User12121 I specifically included the statement "in the form of current" to distinguish between motion stopping entirely (which is never the case since there is always random thermal movement) vs the collective movement of electrons. Is that clear to you now? $\endgroup$
    – Bob D
    Commented Sep 10, 2021 at 16:09
  • $\begingroup$ Yupp thanks a lot ! In general, the behavior of electrons is always intriguing and it's hard to imagine or visualize. Or there is always quantum mechanics for precise understanding and that's an ocean again. $\endgroup$
    – User12121
    Commented Sep 10, 2021 at 17:03
  • $\begingroup$ @User12121 Yeah, but in this case a classical understanding is sufficient $\endgroup$
    – Bob D
    Commented Sep 10, 2021 at 17:06
  • $\begingroup$ @User12121 Also useful to note that the "drift velocity" of the electrons, generating current is far lower than the speed that electronic signals propagate at (some high fraction of the speed of light). That's a very unintuitive thing which can be useful to hold onto $\endgroup$
    – Cort Ammon
    Commented Sep 11, 2021 at 6:05

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