Resistance and Resistivity

Rarely Tested

$$R = \rho \frac{l}{A}$$
Resistance depends on material and geometry.
$$R$$ = resistance (Ω), $$\rho$$ = resistivity (Ω·m), $$l$$ = length (m), $$A$$ = area (m²)
Question 1

A metal wire of cross-sectional area $$0.5\,\mathrm{mm^2}$$ and length $$100\,\mathrm{m}$$ is connected across a battery of e.m.f. $$2\,\mathrm{V}$$ and internal resistance $$1\,\Omega$$. The density, atomic mass and electrical conductivity of the metal are $$6.35\times 10^{3}\,\mathrm{kg\,m^{-3}}$$, $$63.5\,\mathrm{gm/mole}$$ and $$2\times 10^{8}\,\mathrm{mho\,m^{-1}}$$, respectively. Assuming one conduction electron per atom of the metal, the drift velocity (in $$\mathrm{mm\,s^{-1}}$$) of the electrons in the wire is:

[Take Avogadro's number as $$6\times 10^{23}$$ and charge of the electron as $$1.6\times 10^{-19}\,\mathrm{C}$$.]

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