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
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,
- What is the initial current in the circuit?
- 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.