If a current of $80 \ A$ is passing through a straight conductor of length $10 \ m$,then the total momentum of electrons in the conductor is (mass of electron $= 9.1 \times 10^{-31} \ kg$ and charge of electron $= 1.6 \times 10^{-19} \ C$).

Derive the relation between electric current and drift velocity.

$(a)$ Consider the circuit in the figure. How much energy is absorbed by electrons from the initial state of no current (ignore thermal motion) to the state of drift velocity?
$(b)$ Electrons give up energy at the rate of $R I^2$ per second to thermal energy. What time scale would one associate with the energy in problem $(a)$? Given: $n = 10^{29} \, m^{-3}$,length of circuit $l = 10 \, cm$,cross-section $A = (1 \, mm)^2$.

As shown in the figure,a current is passing through a conducting wire. The radius of the cross-section of the wire at point $A$ is $3r$ and at point $B$ is $r$. Find the ratio of the drift velocity at point $A$ to that at point $B$.

$A$ current of $1.344 \, A$ flows through a copper wire of cross-sectional area $1 \, mm^2$. If the number of free electrons per unit volume is $8.4 \times 10^{22} \, cm^{-3}$,then the drift velocity is:

What is relaxation time $(\tau )$? And what is drift velocity $(v_d)$?