Electrical methods

Abstract

Experimentally we know that if we apply a voltage V across the ends of a body of constant cross section, the current (I) is proportional to the applied voltage (V), so that

$$V=RI\quad or\quad R=V/I$$

(2.1)

where R is the constant of the proportionality and is called the resistance of the body. We also know that for a given material the resistance is proportional to its length and inversely proportional to the cross sectional area so that

$$R=\rho L/A\quad or\quad \rho =R.A/L$$

(2.2)

where ρ is called the resistivity of the material and is the resistance of a cube with a side of unit length. The units of resistivity are usually given as ohm — meters (Ω−m) or, more pedantically, Ω−m²/m; this latter system follows from the dimensions of the right hand side of equation 2.2. The formal definition of resistivity is that it is the ratio of the voltage gradient to the current density over a small thin surface element of the medium.