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 $=1.6 \times 10^{-19} \mathrm{C}$ )

The resistivity of a metal is $1 \times 10^{-8} \Omega-\mathrm{m}$. If it contains $9 \times 10^{28}$ electrons per $\mathrm{m}^3$, then the relaxation time of electrons inside the metal is nearly

(electron mass $=9 \times 10^{-31} \mathrm{~kg}$ )

A cylindrical metallic wire is stretched to increase its length in such a way that the metallic wire changes its resistance by $6 \%$. The percentage increase in its length is