When there is an electric current through a conducting wire along its length,then an electric field must exist

Drift velocity $V_d$ varies with the intensity of electric field $E$ as per the relation:

Assume a hypothetical wire in which free electron density changes with temperature in proportionality $n \propto T$,assuming $\tau$ (relaxation time of collision) and dimensions of the wire remain unchanged with increasing temperature. Which one of the resistance $v/s$ temperature graphs is true?

$A$ silicon block at $300\,K$ has a length of $10\,cm$ and a cross-sectional area of $1 \times 10^{-4}\,m^2$. If a $2\,V$ battery is connected across its ends parallel to the length,find the current flowing through it. The electron mobility is $0.14\,m^2V^{-1}s^{-1}$ and the electron number density is $1.5 \times 10^{16}\,m^{-3}$.

There is a current of $1.344 \, A$ in a copper wire whose area of cross-section normal to the length of the wire is $1 \, mm^2$. If the number of free electrons per $cm^3$ is $8.4 \times 10^{22}$, then the drift velocity would be

$A$ current $I$ is passing through a wire having two sections $P$ and $Q$ of uniform diameters $d$ and $d/2$ respectively. If the mean drift velocity of electrons in sections $P$ and $Q$ is denoted by $v_P$ and $v_Q$ respectively,then