11 Electrical Properties of Materials One of the principal characteristics of materials is their ability (or lack of ability)to conduct electrical current.Indeed,materi- als are classified by this property,that is,they are divided into conductors,semiconductors,and nonconductors.(The latter are often called insulators or dielectrics.)The conductivity,o,of dif- ferent materials at room temperature spans more than 25 orders of magnitude,as depicted in Figure 11.1.Moreover,if one takes the conductivity of superconductors,measured at low tempera- tures,into consideration,this span extends to 40 orders of mag- nitude (using an estimated conductivity for superconductors of about 1020 1/0 cm).This is the largest known variation in a phys- ical property and is only comparable to the ratio between the di- ameter of the universe (about 1026 m)and the radius of an elec- tron(10-14m). The inverse of the conductivity is called resistivity,p,that is: p= (11.1) The resistance,R of a piece of conducting material is propor- tional to its resistivity and to its length,L,and is inversely pro- portional to its cross-sectional area,A: R=L:P A (11.2) The resistance can be easily measured.For this,a direct current is applied to a slab of the material.The current,I,through the sample (in amperes),as well as the voltage drop,V,on two po- tential probes (in volts)is recorded as depicted in Figure 11.2.11 One of the principal characteristics of materials is their ability (or lack of ability) to conduct electrical current. Indeed, materi￾als are classified by this property, that is, they are divided into conductors, semiconductors, and nonconductors. (The latter are often called insulators or dielectrics.) The conductivity, , of dif￾ferent materials at room temperature spans more than 25 orders of magnitude, as depicted in Figure 11.1. Moreover, if one takes the conductivity of superconductors, measured at low tempera￾tures, into consideration, this span extends to 40 orders of mag￾nitude (using an estimated conductivity for superconductors of about 1020 1/# cm). This is the largest known variation in a phys￾ical property and is only comparable to the ratio between the di￾ameter of the universe (about 1026 m) and the radius of an elec￾tron (1014 m). The inverse of the conductivity is called resistivity, , that is: 
1 . (11.1) The resistance, R of a piece of conducting material is propor￾tional to its resistivity and to its length, L, and is inversely pro￾portional to its cross-sectional area, A: R
L A   . (11.2) The resistance can be easily measured. For this, a direct current is applied to a slab of the material. The current, I, through the sample (in ampères), as well as the voltage drop, V, on two po￾tential probes (in volts) is recorded as depicted in Figure 11.2. Electrical Properties of Materials