The potential difference across a conducting wire of length $20 \ cm$ is $30 \ V$. If the electron mobility is $2 \times 10^{-6} \ m^2 \ V^{-1} \ s^{-1}$,then the drift velocity of the electrons is

If a current of $80 \ A$ is passing through a straight conductor of length $10 \ m$,then the total momentum of electrons in the conductor is (mass of electron $= 9.1 \times 10^{-31} \ kg$ and charge of electron $= 1.6 \times 10^{-19} \ C$).

$A$ current flows in a wire of circular cross-section with the free electrons travelling with a mean drift velocity $\vec v$. If an equal current flows in a wire of twice the radius,the new mean drift velocity is:

$A$ metal has $9 \times 10^{28}$ conduction electrons per $m^3$ and its resistivity is $1 \times 10^{-8} \Omega \cdot m$. If the drift speed of an electron in the metal is $1.6 \times 10^6 \ m/s$, then its mean free path is (mass of electron $= 9 \times 10^{-31} \ kg$ and charge of electron $= 1.6 \times 10^{-19} \ C$). (in $nm$)

$A$ cylindrical resistor of radius $7.0 \, mm$ and length $4.0 \, cm$ is made of a material that has a resistivity of $10^{-6} \, \Omega \cdot m$. If the energy is dissipated at a rate of $1.54 \, W$ in the resistor, then the current density is:

$A$ 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 $1.5 \times 10^{16}\,m^{-3}$.