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I'm trying to understand why when writing the differential equation of a discharging RC circuit [itex]V_C-Ri(t)=0 \to q(t)/C - Ri(t)=0[/itex] we replace [itex]i(t)[/itex] with [itex]-\frac{dq(t)}{dt}[/itex].

I read many threads but I don't understand the physics behind this. The usual answers I read are something like "by using the passive sign convention" or "because the current must be positive".

I'd like to solve this problem because it is driving me crazy!