Assume a hypothetical wire in which free electron density changes with temperature in proportionality $n \propto T$,assuming $\tau$ (relaxation time of collision) and dimensions of the wire remain unchanged with increasing temperature. Which one of the resistance $v/s$ temperature graphs is true?

$A$ $1 \mu A$ beam of protons with a cross-sectional area of $0.5 \text{ mm}^2$ is moving with a velocity of $3 \times 10^4 \text{ m/s}$. The charge density of the beam is:

Two wires $A$ and $B$ of the same material have lengths $L_A, L_B$ and radii $R_A, R_B$ and drift velocities $v_A, v_B$ respectively. Both wires carry the same current. If $L_A = L_B$ and $R_A = 2R_B$,then the value of $\left(\frac{v_A}{v_B}\right)$ is:

The drift velocity of electrons in a current-carrying wire of radius $r$ is $v$. If we want a drift velocity of $2v$ in a wire of the same material but with half the radius,what current must be passed through it?

$A$. The drift velocity of electrons decreases with the increase in the temperature of a conductor.
$B$. The drift velocity is inversely proportional to the area of cross-section of a given conductor.
$C$. The drift velocity does not depend on the applied potential difference to the conductor.
$D$. The drift velocity of an electron is inversely proportional to the length of the conductor.
$E$. The drift velocity increases with the increase in the temperature of a conductor.
Choose the correct answer from the options given below:

At room temperature,copper has a free electron density of $8.4 \times 10^{28} \, m^{-3}$. The copper conductor has a cross-section of $10^{-6} \, m^2$ and carries a current of $5.4 \, A$. The electron drift velocity in copper is: