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I encountered a problem as a part of the solution of which I needed to get the i-V relation across a solenoid to gain some intution in the other parts of the problem, which is the well known expression

V_{L}=Ldi_{L}/dt, where V and i are referenced with respect to the passive sign convention.

Nothing tricky here, just basic stuff - however I wanted to quickly verify this before I moved on in the problem. The following is a simple MSpaint sketch that I have just created for illustrative purposes

The rest of the details are in the above picture. The question I had in mind is why I am not able to derive the simple relation V_{L}=Ldi_{L}/dt for an inductor (solenoid in this case), even though I referenced everything in line with the passive sign convention?

Thanks!

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# Inductance of a coil (negative inductance?)

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