Question

Write a relation between current and drift velocity of electrons in a conductor.use this relation to explain how the resistance of a conductor changes with the rise in temperature?

Answer 1

$$\begin{gathered} \mathrm{Relation}\mathrm{between}\mathrm{current}\mathrm{and}\mathrm{drift}\mathrm{velocity}: \\ \mathrm{I}=\mathrm{n}\mathrm{e}\mathrm{A}{\mathrm{v}}_{\mathrm{d}} \\ \mathrm{n}=\mathrm{Number}\mathrm{of}\mathrm{electrons} \\ \mathrm{e}=\mathrm{Charge}\mathrm{of}\mathrm{electrons} \\ \mathrm{A}=\mathrm{Cross}-\mathrm{sectional}\mathrm{area} \\ {\mathrm{v}}_{\mathrm{d}}=\mathrm{Drift}\mathrm{velocity} \\ \mathrm{Resistance}\mathrm{of}\mathrm{conductor}\mathrm{with}\mathrm{change}\mathrm{in}\mathrm{temperature}: \\ *\mathrm{With}\mathrm{the}\mathrm{increase}\mathrm{in}\mathrm{temperature},\mathrm{the}\mathrm{drift}\mathrm{velocity}\mathrm{of}\mathrm{electrons}\mathrm{and}\mathrm{the}\mathrm{collision} \\ \mathrm{between}\mathrm{electrons}\mathrm{increases}. \\ *\mathrm{Due}\mathrm{to}\mathrm{increase}\mathrm{in}\mathrm{collision}\mathrm{between}\mathrm{the}\mathrm{electrons},\mathrm{the}\mathrm{resistance}\mathrm{of}\mathrm{the}\mathrm{conductor} \\ \mathrm{increases}. \\ *\mathrm{Hence},\mathrm{we}\mathrm{can}\mathrm{conclude}\mathrm{that}\mathrm{the}\mathrm{resistance}\mathrm{of}\mathrm{a}\mathrm{conductor}\mathrm{increases}\mathrm{with}\mathrm{increase} \\ \mathrm{in}\mathrm{temperature}. \end{gathered}$$