Derive the relation between electric current and drift velocity.

$A$ wire has a non-uniform cross-section as shown in the figure. $A$ steady current flows through it. The drift speed of electrons at points $P$ and $Q$ is $v_P$ and $v_Q$ respectively.

$A$ current of $10 \, A$ is passing through an aluminum wire of cross-sectional area $4 \times 10^{-6} \, m^{2}$. If the density of aluminum is $2.7 \, g/cm^{3}$ and it provides $1$ free electron per atom for conduction,find the drift speed of the electrons in $\times 10^{-4} \, m/s$. (Given: molecular weight of aluminum = $27 \, g/mol$,Avogadro's number $N_{A} = 6.022 \times 10^{23} \, mol^{-1}$)

When $5\ V$ potential difference is applied across a wire of length $0.1\ m$,the drift speed of electrons is $2.5 \times 10^{-4} \ m/s$. If the electron density in the wire is $8 \times 10^{28} \ m^{-3}$,the resistivity of the material is close to:

$A$ uniform copper wire carries a current $i$ amperes and has $p$ carriers per meter$^3$. The length of the wire is $\lambda$ meters and its cross-section area is $s$ meter$^2$. If the charge on a carrier is $q$ coulombs,the drift velocity in $ms^{-1}$ is given by

In a wire with a cross-sectional area of $1 \, cm^2$ carrying a current of $24 \, mA$,the electron number density is $3 \times 10^{23} \, m^{-3}$. What is the drift velocity?