The resistivity of a silver wire increases from at to at

PHYSICS · Single correct · A Level · Physics · Electricity · Electricity

Problem

The resistivity

\rho

of a silver wire increases from

1.6\times10^{-8}\,\Omega\,\text{m}

20\,^{\circ}\!\text{C}

2.4\times10^{-8}\,\Omega\,\text{m}

100\,^{\circ}\!\text{C}

. Which statement about the wire’s electrical conductivity

\sigma

(where

\sigma = 1/\rho

) is most accurate? (a) The conductivity increases by a factor of about

\dfrac{2.4}{1.6}

because the electrons gain kinetic energy at the higher temperature. (b) The conductivity decreases by a factor of about

\dfrac{2.4}{1.6}

because increased lattice vibrations hinder electron movement. (c) The conductivity decreases by a factor of about

\dfrac{1.6}{2.4}

because increased lattice vibrations hinder electron movement. (d) The conductivity first decreases, then increases beyond

60\,^{\circ}\!\text{C}

as additional electron–hole pairs are thermally generated.