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:

Cross-sectional area of a copper wire is equal to the area of a square of length $2 \ mm$. If this copper wire draws $8 \ A$ electric current,then find the drift velocity of free electrons. The number density of electrons in the copper wire is $8 \times 10^{28} \ m^{-3}$.

Current density in a cylindrical wire of radius $R$ varies with radial distance as $J(r) = \beta(r + r_0)^2$. The current through the shaded section of the wire shown in the figure is:

$A$ current of $5\; A$ is passing through a non-linear magnesium wire of cross-section $0.04\; m^2$. At every point,the direction of current density is at an angle of $60^{\circ}$ with the unit vector of the area of cross-section. The magnitude of the electric field at every point of the conductor is .... $V/m$ (Resistivity of magnesium is $\rho = 44 \times 10^{-8}\, \Omega m$).

$A$ cylindrical resistor is connected across a battery $\varepsilon$. The cylinder has a uniform free electron density, and the middle part of the cylinder has a larger radius as shown in the figure. Which of the following graphs represents the variation of $V_d$ (drift velocity) with respect to $x$ (distance along the length of the resistor)?

$A$ 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: