Charge passing through a conductor of cross-section $0.3 \, m^2$ is given by $q = (3t^2 + 5t + 2) \, C$ where '$t$' is in seconds. The drift velocity at $t = 2 \, s$ is (Concentration of electrons in the conductor $= 2 \times 10^{25} \, m^{-3}$)

$A$ metallic block has no potential difference applied across it. What is the mean velocity of free electrons in terms of $T$ (absolute temperature of the block)?

$A$ copper wire of length $1\, m$ and radius $1\, mm$ is joined in series with an iron wire of length $2\, m$ and radius $3\, mm$ and a current is passed through the wires. The ratio of the current density in the copper and iron wires is

In a metallic conductor,under the effect of an applied electric field,the free electrons of the conductor

Consider a metallic cube of edge length $L$. Its resistance,$R$,measured across its opposite faces is $R = \frac{m_e v}{n e^2 L^2}$,where $n$ is the number density and $v$ is the drift speed of electrons in the cube,and $e$ and $m_e$ are the charge and mass of an electron respectively. Assuming the de-Broglie wavelength of the electron to be $L$,the maximum resistance of the sample is closest to ............. $\Omega$ ($e = 1.60 \times 10^{-19} \, C$; $m_e = 9.11 \times 10^{-31} \, kg$; Planck's constant,$h = 6.63 \times 10^{-34} \, Js$)

The drift velocity does not depend upon