$A$ current $I$ flows through a uniform wire of diameter $d$ when the mean electron drift velocity is $V$. The same current will flow through a wire of diameter $d/2$ made of the same material if the mean drift velocity of the electron is:

$A$ copper wire has a square cross-section,$2.0 \, mm$ on a side. It carries a current of $8 \, A$ and the density of free electrons is $8 \times 10^{28} \, m^{-3}$. The drift speed of electrons is equal to

The electric field $E$,current density $J$ and conductivity $\sigma$ of a conductor are related as

$A$ current of $1.344 \, A$ flows through a copper wire of cross-sectional area $1 \, mm^2$. If the number of free electrons per unit volume is $8.4 \times 10^{22} \, cm^{-3}$,then the drift velocity is:

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,$h = 6.63 \times 10^{-34} \, Js$)

The current density in a cylindrical wire of radius $r = 4.0 \, mm$ is $J = 1.0 \times 10^{6} \, A/m^{2}$. The current through the outer portion of the wire between radial distances $r/2$ and $r$ is $x \pi \, A$,where $x$ is ..........