Define the term 'resistivity' and 'conductivity and state their SI units. Draw a graph showing the variation of resistivity with temperature for a typical semiconductor.

Explanation

The units of conductance and conductivity are simen (denoted by S) and simen `"meter"^(-1)` (denoted by `S m^(-1)`) respectively. We know that conductance `= 1//"resistance"`.
`:.` 1 simen is the coductance of a conductor of resistance 1 ohm.
We know, electrical conductivity, `sigma = 1/rho = l/(RA)`
If `l= l m, R = 1 Omega, A = 1 m^(2)` then `sigma= 1 S m^(-1)`
Thus `1 S m^(-1)` is the electrical conductivity of a conductor of length 1 m, area of cross-section `1 m^(2)` and resistance `1 Omega` or conductance 1S.
Diamensional formula of conductance,
`G=(1)/(R)=(I)/(V)=([A])/([ML^(2)T^(-3)A^(-1)])=[M^(-1)L^(-2)T^(3)A^(2)]`
Dimensional formula of coductivity,
`sigma = 1/rho =l/(RA) = [M^(-1)L^(-2)T^(3)A^(2)] xx L/L^(2)`
`[M^(-1)L^(-3)T^(3)A^(2)]`