Physics - Current Electricity Question with Solution | TestHub

Statement 1 is true. As temperature increases, the thermal vibrations of lattice ions increase, leading to more frequent collisions of free electrons with the lattice. This decreases the average relaxation time $\tau$. Since drift velocity $v_d=\frac{eE\tau }{m}$, a decrease in $\tau$ for a given electric field $E$ results in a decrease in $v_d$. Statement 2 is false. The number density of free electrons ($n$) in a metallic conductor is largely independent of temperature. The increase in resistance with temperature is primarily due to the decrease in relaxation time $\tau$, which increases resistivity $\rho =\frac{m}{n{e}^2\tau }$.