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Thinking in terms cause and effect in this case are at the root of your puzzlement. For an ideal inductor, the voltage across, at any instant $t$, is proportional to the time rate of change of current at the same instant $t$. If you wish to see this as cause and effect, then look at the integral formulation: i_L(t) = \frac{1}{L}\int_{-\infty}^t ...

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You're getting confused by what sets the voltage across the inductor. A (perfect) voltage source supplies whatever current is required to maintain a given voltage across its output terminals. So, in that case, the current is what the source varies in order to keep the voltage constant. When you connect a device to a voltage source, the voltage across the ...

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I think you're drawing a parallel where none exists. Mutual inductance is where a changing current in one inductor influences the current in an adjacent inductor; this happens because it's easy for the (also changing) magnetic field of one inductor goes through another inductor (e.g. a transformer). Mutual capacitance, instead, is just a measure of the ...

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