Two identical conductors are kept at the same temperature. If the ratio of the potential difference across them is $1 : 2$,what will be the ratio of their drift velocities?

$A$ current of $10\, A$ exists in a wire of cross-sectional area of $5\, mm^{2}$ with a drift velocity of $2 \times 10^{-3}\, m/s$. The number of free electrons in each cubic meter of the wire is ..........

$A$ silver wire of length $3 \,m$ and of cross-sectional area $6.14 \times 10^{-6} \,m^2$ carries a current of $6 \,A$. The atomic weight and density of silver are $108 \,g/mol$ and $10500 \,kg/m^3$,respectively. $A$ silver atom contributes one free electron for conduction. The Avogadro number is $6.023 \times 10^{23} /mol$. The drift velocity of electrons in silver is close to:

The quantities that do not change when a resistor connected to a battery is heated due to the current are:
$(A)$ drift speed
$(B)$ resistivity
$(C)$ resistance
$(D)$ number of free electrons

The current density in a cylindrical wire of radius $4 \; mm$ is $4 \times 10^{6} \; A \cdot m^{-2}$. The current through the outer portion of the wire between radial distance $\frac{R}{2}$ and $R$ is $\dots \; \pi \; A$.

$A$ metal has $9 \times 10^{28}$ conduction electrons per $m^3$ and its resistivity is $1 \times 10^{-8} \Omega \cdot m$. If the drift speed of an electron in the metal is $1.6 \times 10^6 \ m/s$, then its mean free path is (mass of electron $= 9 \times 10^{-31} \ kg$ and charge of electron $= 1.6 \times 10^{-19} \ C$). (in $nm$)