Q.Two wires A and B with circular cross section are made up of the same material with equal lengths. Suppose $R_A = 3R_B$, then what is the ratio of radius of wire A to that of B?

Definition. A conductor's resistance is $R=l/(\sigma A)$, where $\sigma$ is its conductivity; the reciprocal of conductivity is defined as the resistivity, $\rho=1/\sigma$, letting resistance be rewritten in the commonly used form

Resistance is thus directly proportional to a conductor's length l and inversely proportional to its cross-sectional area A -- setting $l=1$ m and $A=1\ \text{m}^2$ shows $R=\rho$, so the electrical resistivity of a material is the resistance offered by a sample of that material having unit length and unit cross-sectional area. The SI unit of $\rho$ is the ohm-metre ($\Omega\text{m}$).

Sorting materials by resistivity. Because resistivity is a pure material property, independent of any particular sample's shape or size, it is exactly what is used to classify materials into three broad categories: conductors (lowest resistivity, of order $10^{-8}\ \Omega\text{m}$ for metals like silver, copper, aluminium, tungsten and iron), insulators (highest resistivity, spanning roughly $10^{10}$ to $10^{16}\ \Omega\text{m}$ for materials like glass, hard rubber, NaCl and fused quartz), and semiconductors (an intermediate range, exemplified by germanium at 0.46 $\Omega\text{m}$ and silicon at 640 $\Omega\text{m}$ -- both far higher than any metal, yet far lower than any true insulator). …