I've seen 2 different formulas being used for the voltage of a coil in a circuit. The first one is $$U_L=L\cdot\dot{I}$$ and the second one is $$U_L=-L\cdot\dot{I}$$ The first formula was used in a circuit with a resistance and a coil, to calculate the total voltage as $$U_0 = U_R + U_L$$ and the second formula has been used everywhere else so far.
I'm not which formula I should use in which context. Any help is appreciated.
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1 Answer
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In the context of AC circuits, voltage on an element means usually "decrease of electric potential along the pre-chosen positive direction". For an ideal inductor (one without ohmic resistance), this potential drop is always with + sign: $$ p.d. = L\frac{dI}{dt}. $$
This result is because for a path through an ideal inductor, the effect of the potential drop completely cancels out the effect of the induced electromotive force $\mathscr{E}_i$, which is known (both for ideal and real inductors) to be given by $$ \mathscr{E}_i = - L\frac{dI}{dt}. $$ The minus sign here is to express correctly the Lenz law: the induced electromotive force in such direction that it acts to prevent the change of current.
answered May 25, 2021 at 19:11