Electric Circuits

What is electric current primarily defined as?

A wire carries a current $I$. If the number of charge carriers per unit volume ($n$) is doubled, the charge of each carrier ($q$) is halved, the drift velocity ($v_d$) remains the same, and the cross-sectional area ($A$) is doubled, what is the new current $I'$ in terms of the original current $I$?

A cylindrical wire has a radius that varies along its length according to the function $r(x) = R_0 + ax$, where $R_0$ and $a$ are constants, and $x$ is the distance along the wire. If the charge carrier density $n$, charge $q$, and drift velocity $v_d$ are constant, what is the expression for the current $I$ at position $x$?

A copper wire has a charge carrier density of $8.5 \times 10^{28} \text{ m}^{-3}$ and each electron has a charge of $1.6 \times 10^{-19} \text{ C}$. If the drift velocity of the electrons is $7 \times 10^{-4} \text{ m/s}$, what is the current density in the wire?

A cylindrical conductor of radius $R$ has a current density given by $J(r) = J_0(1 - (r/R)^2)$, where $J_0$ is a constant. What is the total current through the conductor?

A copper wire has a charge carrier density of $8.5 \times 10^{28} \text{ m}^{-3}$. If each charge carrier has a charge of $1.6 \times 10^{-19} \text{ C}$, and the drift velocity is $5 \times 10^{-4} \text{ m/s}$, what is the current flowing through a wire with a cross-sectional area of $4 \times 10^{-6} \text{ m}^2$?

In a circuit segment, electrons are observed to be moving from point B to point A. Which of the following statements is true regarding the conventional current?

A cylindrical conductor has a non-uniform current density given by $J(r) = Ar^2$, where $A$ is a constant and $r$ is the distance from the axis of the cylinder. If the radius of the cylinder is $R$, what is the total current flowing through the conductor?

A long cylindrical wire of radius $R$ has a current density that varies as $J(r) = br^3$, where $b$ is a constant. Find the total current flowing through the wire.

What is the direction of conventional current?