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It seems to me that the typical relationship between V, I and R is a
relationship between scalars and, as such, does not need a minus
sign. Is this correct?
On the other hand, can we start with E = rho j (which is a vector
relationship) and replace E with - Del V, rho = AR/L, and I = JA, to
get a vector equation with Del V, L, R and I? In that case, the
vector equation would necessarily have a minus sign, no?