0
$\begingroup$

Kirchhoff's loop law states that the sum of emfs equals the sum of voltage drops around a loop. In the electrostatic case, it would make sense in that the sum of potential differences should be zero around a closed loop. More generally however, we can have other sources of emf, like motional or chemical - in which case the justification for the law seems to be: the work required to move a charge around the loop is zero.

This makes sense if current is constant, as charge carriers stay at the same speed and hence cannot gain kinetic energy as we leave the circuit closed. However, it's not obvious to me that a charge cannot gain energy at all when current is changing. Say we have an AC circuit - is it not possible that charges are gaining energy when going around a loop? That would be consistent with the fact that the current is changing. Or is it the case that this "equilibrium" happens much faster than the current itself changes? What if we consider the limit of very high frequencies?

$\endgroup$

1 Answer 1

0
$\begingroup$

Relevant: Circuit Loop Law Doubt

To build on that answer: KVL comes from Faraday's law, which states that EMF around a loop is equal to the rate of change of magnetic flux. If we can model the magnetic field as coming from an ideal lumped inductor, then KVL is exact, since the change of flux is accounted for by the inductor voltage $V=L \frac{dI}{dt}$. If there is some external magnetic field, or the circuit cannot be modeled with lumped inductance, then KVL is only approximate.

$\endgroup$
1
  • $\begingroup$ Does Faraday's law include emf sources such as batteries? $\endgroup$
    – user35013
    Mar 17, 2023 at 11:29

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.