If the ratio of the radii of two wires of the same material is $1 : 2$ and the ratio of the current flowing through them is $4 : 1$,what is the ratio of their drift velocities?

Consider a metallic cube of edge length $L$. Its resistance,$R$,measured across its opposite faces is $R = \frac{m_e v}{n e^2 L^2}$,where $n$ is the number density and $v$ is the drift speed of electrons in the cube,and $e$ and $m_e$ are the charge and mass of an electron respectively. Assuming the de-Broglie wavelength of the electron to be $L$,the maximum resistance of the sample is closest to ............. $\Omega$ ($e = 1.60 \times 10^{-19} \, C$; $m_e = 9.11 \times 10^{-31} \, kg$; Planck's constant,$h = 6.63 \times 10^{-34} \, Js$)

$A$ copper wire of length $1 \,m$ and uniform cross-sectional area $5 \times 10^{-7} \,m^{2}$ carries a current of $1 \,A$. Assuming that there are $8 \times 10^{28}$ free electrons per $m^{3}$ in copper,how long will an electron take to drift from one end of the wire to the other?

$(a)$ Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area $1.0 \times 10^{-7} \; m^{2}$ carrying a current of $1.5 \; A$. Assume that each copper atom contributes roughly one conduction electron. The density of copper is $9.0 \times 10^{3} \; kg/m^{3}$ and its atomic mass is $63.5 \; u$.
$(b)$ Compare the drift speed obtained above with,$(i)$ thermal speeds of copper atoms at ordinary temperatures,$(ii)$ speed of propagation of electric field along the conductor which causes the drift motion.

The lengths of two wires made of the same material are in the ratio $2:3$ and their radii are in the ratio $1:2$. If the two wires are connected in parallel to a battery,then the ratio of the drift velocities of free electrons in the two wires is

Which of the following is the unit of mobility of an electron in a conductor?