The relationship between current ($I$) and drift velocity ($v_d$) is given by the formula $I = nAe v_d$ . The time ($t$) taken for an electron to drift across the length ($l$) of the wire is $t = \frac{l}{v_d}$. Substituting $v_d$ from the current equation, we get $t = \frac{n A e l}{I}$.

Given: $n = 8.5 \times 10^{28} \text{ m}^{-3}$ $A = 2.0 \times 10^{-6} \text{ m}^2$ $e = 1.6 \times 10^{-19} \text{ C}$ $l = 3.0 \text{ m}$ $I = 3.0 \text{ A}$

Calculation: $t = \frac{(8.5 \times 10^{28})(2.0 \times 10^{-6})(1.6 \times 10^{-19})(3.0)}{3.0}$ $t = 8.5 \times 2.0 \times 1.6 \times 10^{3}$ $t = 27.2 \times 10^3 \text{ s} = 2.72 \times 10^4 \text{ s}$.