An ionization chamber with parallel conducting plates as anode and cathode has $5 \times 10^7$ electrons and the same number of singly-charged positive ions per $cm^3$. The electrons are moving at $0.4\, m/s$. The current density from anode to cathode is $4\,\mu A/m^2$. The velocity of positive ions moving towards cathode is ............. $m/s$. [$AIPMT$ $1992$]

Assume a hypothetical wire in which free electron density changes with temperature in proportionality $n \propto T$,assuming $\tau$ (relaxation time of collision) and dimensions of the wire remain unchanged with increasing temperature. Which one of the resistance $v/s$ temperature graphs is true?

There is a current of $20 \, A$ in a copper wire of $10^{-6} \, m^2$ area of cross-section. If the number of free electrons per cubic meter is $10^{29}$,then the drift velocity is:

An insulating pipe of cross-section area $A$ contains an electrolyte which has two types of ions with charges $-e$ and $+2e$. $A$ potential difference applied between the ends of the pipe results in the drifting of the two types of ions,having drift speeds $v$ (for $-e$ ion) and $v/4$ (for $+2e$ ion). Both ions have the same number density $n$. The current flowing through the pipe is:

$A$ current of $2\,A$ flows through a wire of cross-sectional area $25.0\,mm^2$. The number of free electrons per cubic meter is $2.0 \times 10^{28}$. The drift velocity of the electrons is $...............\times 10^{-6}\,ms^{-1}$ (given,charge on electron $= 1.6 \times 10^{-19}\,C$).

$A$ 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 ......