Drift of Electrons and the Origin of Resistivity

Which of the following relations between the drift velocity $v_d$ and electric field $E$ obeys ohm's law.

Two cylindrical rods of uniform cross-section area $A$ and $2A,$ having free electrons per unit volume $2n$ and $n,$ respectively, are joined in series. A current $I$ flows through them in steady-state. Then, the ratio of drift velocity of free electrons in the left rod to drift velocity of electrons in the right rod is,

The drift velocity of electrons in a conducting wire is of the order of $1 \mathrm{mm} {\mathrm{s}}^{-1}$. Yet the bulb glows very quickly after the switch is put on because

Drift speed of electrons, when $1.5 \mathrm{A}$ current flows in a copper wire of cross section $5 {\mathrm{mm}}^2$ is $v_d.$ If the electron density in copper is $9\times {10}^{28} {\mathrm{m}}^{-3}$ the value of $v_d$ in $\mathrm{mm} {\mathrm{s}}^{-1}$ is close to (Take charge of an electron to be $=1.6\times {10}^{-19} \mathrm{C}$)

A current $i$ is flowing through the wire of diameter $\left(d\right)$ having drift velocity of electrons $v_d$ in it. What will be new drift velocity when diameter of wire is made $\frac{d}{4}?$

When the temperature of a conductor increase the ratio of conductivity and resistivity ______.

The area of cross-section of a current carrying conductor is $A_0$ and $\frac{A_0}{4}$ at section $\left(1\right)$ and $\left(2\right)$ respectively. If $v_{d_1}$ and $v_{d_2}$ be the drift velocity at sections $\left(1\right)$ and $\left(2\right)$ respectively, then

Drift velocity, $v_d$, varies with the intensity of electric field as per the relation,

A constant current source is connected to a wire. If the wire is stretched to twice its length, then the drift velocity:

Two wires of the same material but of different diameters carry the same current $i$. If ratio of their diameters is $1:2$, then the corresponding ratio of their mean drift velocities will be,

A metallic resistor is connected across a battery. If the number of collisions of the free electrons with the lattice is some how decreased in the resistor (for example by cooling it), the current will,

There is a current of $0.21 \mathrm{A}$ in a copper wire whose area of cross-section is ${10}^{-6} {\mathrm{m}}^2$. If the number of free electrons per ${\mathrm{m}}^3$ is $8.4\times {10}^{28}$, then find the drift velocity,

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

A potential difference of $V$ is applied at the ends of a copper wire of length $l$ and diameter $d$. On doubling only $d$, the drift velocity,

The drift velocity of the electrons in a copper wire of length $2 \mathrm{m}$ under the application of a potential difference of $220 \mathrm{V}$ is $0.5 \mathrm{m} {\mathrm{s}}^{-1}$. Their mobility (in$\mathrm{ }{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$) is

If the free electron density be $n$ and relaxation time be $\tau$, the electrical conductivity of a conductor may be expressed as