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I am a grade 12th student studying about inductors and RLC circuits for the first time. While studying I got stuck with the idea of an active inductor being connected to an inactive inductor. Something like the situation shown here enter image description here

Now the middle inductor of inductance L is in position 1, connected across a cell for a long time such that it’s been allowed to attain a steady current. Now it’s switched to position 2, to a circuit with a similar resistance (the inductors are considered resistance less) and a similar inductor, for convenience I considered the mutual induction to be 0.

Now, when the circuit is switched to position 2, the active inductor would like to prevent the change i of flux through it and start using some of its stored energy to keep the current flowing, thus maintaining the flux. Whereas the second inductor which is initially inactive would like to prevent the change of flux through it and produces an opposing EMF to resist the change in flux.

Now my question is, in such a scenario,

  1. What is the initial current in the circuit?
  2. And What kind of a differential equation can I use to describe this circuit?

I added the resistance in position 2 for the sake of “realism”, but if it complicates things, please feel free to ignore the resistance and explain assuming ideal inductors only.

Thank you in advance.

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  • \$\begingroup\$ This never happens: and produces an opposing current to resist the change in flux \$\endgroup\$
    – Andy aka
    Commented Aug 30, 2023 at 15:30
  • \$\begingroup\$ @Andyaka my bad, I should’ve written EMF, instead I wrote current. Thank you for pointing it out. I will correct it. \$\endgroup\$ Commented Aug 30, 2023 at 15:34

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This is a circuit that can't be modeled with ideal components, because the non-idealities are critical to its behavior. Without including non-idealities the analysis leads to a logical paradox, as you have discovered. An ideal inductor can not change its current instantaneously but you have set up a model where one or both of the inductors must do so because their currents must be equal.

A similar situation occurs if you have two capacitors charged to different potentials and switch them into a parallel connection.

To model your inductor circuit you need to account for the interwinding capacitance of the inductors. This appears as a parasitic capacitance in parallel with each inductor. Once you have included these capacitors then the paradox in the circuit analysis is eliminated.

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  • \$\begingroup\$ Oh that makes a lot of sense, Thank you very much!!! it clears up my doubt. \$\endgroup\$ Commented Aug 30, 2023 at 15:31

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