What is the SI unit of resistivity?

State the relation between conductivity \(\sigma\) and resistivity \(\rho\).

For an ohmic material with positive resistivity, are \(\vec E\) and \(\vec J\) parallel or anti-parallel?

A material has \(\rho=1.7\times10^{-8}\,\Omega\,\mathrm{m}\) and \(J=2.0\times10^6\,\mathrm{A\,m^{-2}}\). Find \(E\).

A material has conductivity \(5.0\times10^7\,\mathrm{S\,m^{-1}}\). Find its resistivity.

A wire has length \(2.0\,\mathrm{m}\), area \(1.0\times10^{-6}\,\mathrm{m^2}\), and resistivity \(2.5\times10^{-8}\,\Omega\,\mathrm{m}\). Find \(V/I\).

A metal has \(\rho_0=1.6\times10^{-8}\,\Omega\,\mathrm{m}\) at \(20^\circ\mathrm{C}\) and \(\alpha=4.0\times10^{-3}\,\mathrm{K^{-1}}\). Estimate \(\rho\) at \(70^\circ\mathrm{C}\).

A cylindrical wire is stretched to twice its original length while its volume stays constant. Assuming resistivity is unchanged, by what factor does \(V/I\) change?

A conductor is tapered so its cross-sectional area varies as \(A(x)=A_0(1+x/L)\) from \(x=0\) to \(L\). With resistivity \(\rho\), derive the resistance by integrating small slices.

A wire has \(\rho(T)=\rho_0[1+\alpha(T-T_0)]\) and temperature varies linearly from \(T_0\) at one end to \(T_0+\Delta T\) at the other. Derive the resistance for uniform area \(A\) and length \(L\).