A copper wire has a diameter of \(0.20 \mathrm{~mm}\) and is \(\ell_{\text {wirc }}=10 \mathrm{~m}\) long.

(a) What is the resistance of the wire?

(b) The wire is cut into \(N\) identical pieces, and the pieces are connected in parallel to form a single resistor. What is the minimum value of \(N\) that gives this resistor a resistance smaller than \(R_{\text {resistor }}=1.0 \Omega\) ? [The conductivity of copper is \(5.9 \times 10^{7} \mathrm{~A} /(\mathrm{V} \cdot \mathrm{m})\).]