$A$ 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 $N_{A} = 6.022 \times 10^{23} \, mol^{-1}$)

The mechanism of the heat produced in a conductor when an electric current flows through it can be explained on the basis of

In a particle accelerator,a current of $500 \,\mu A$ is carried by a proton beam in which each proton has a speed of $3 \times 10^7 \,m/s$. The cross-sectional area of the beam is $1.50 \,mm^2$. The charge density in this beam (in $C/m^3$) is close to

$A$ cylindrical conductor of diameter $0.1 \text{ mm}$ carries a current of $90 \text{ mA}$. The current density (in $\text{Am}^{-2}$) is (take $\pi \simeq 3$):

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

Which of the following quantities does not change when a resistor connected to a battery is heated due to the current?