Find the mobility of electron in a wire, if its average collision time is $9.1 \times 10^{-15} \mathrm{~s}$. (Charge of electron $=1.6 \times 10^{-19} \mathrm{C}$ and mass of electron $=9.1 \times 10^{-31} \mathrm{~kg}$ )

Statement I The temperature coefficient of resistance for most of metals in pure form is positive.

Statement II A metal wire 2 mm in diameter carries a charge of $360 \pi \mathrm{C}$ in two hours. If the metal contains $5 \times 10^{22}$ free electrons $/ \mathrm{cm}^3$, then drift velocity of the electrons in the wire is $6.25 \times 10^{10} \mathrm{~m} / \mathrm{s}$.

Statement III Semiconductors like pure germanium does not obey Ohm's law for all range of electric field values.

Which of the following is correct?

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

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