$A$ wire of non-uniform cross-section is carrying a steady current. Along the wire,

In a wire of circular cross-section with radius $r$,free electrons travel with a drift velocity $V$ when a current $I$ flows through the wire. What is the current in another wire of half the radius and of the same material when the drift velocity is $2V$?

$A$ cylindrical wire of radius $0.5 \, mm$ and conductivity $5 \times 10^{7} \, S/m$ is subjected to an electric field of $10 \, mV/m$. The expected value of current in the wire will be $x^{3} \, \pi \, mA$. The value of $x$ is ......

$A$ copper wire of length $1 \ m$ and radius $1 \ mm$ is connected in series with an iron wire of length $2 \ m$ and radius $3 \ mm$. If a current flows through both wires,the ratio of the current density in the copper wire to that in the iron wire will be:

Choose the correct option with respect to the statements $A$ and $B$:
$(A)$: When no electric field is applied across a conductor,the path of free electrons between two successive collisions in it is straight.
$(B)$: When an electric field is applied across a conductor,the drift velocity of electrons is independent of time.

$A$ conductor of length $100 \, cm$ and area of cross-section $1 \, mm^2$ carries a current of $5 \, A$. If the resistivity of the material of the conductor is $3.0 \times 10^{-8} \, \Omega \cdot m$, then the electric field across the conductor is (in $ \, V/m$)