What is relaxation time?

$(a)$ 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 $A = (1 \, mm)^2$.

Assertion : The electric bulb glows immediately when the switch is on.
Reason : The drift velocity of electrons in a metallic wire is very high.

The drift velocity of an electron is $v_d$ in a conductor of area of cross-section $A$ and carries a current $I$. Now,the area of cross-section and current flowing through the conductor are doubled,then the new drift velocity of the electron is . . . . . . .

An electric current flows along an insulated strip $PQ$ of a metallic conductor. The current density in the strip varies as shown in the graph. Which one of the following statements could explain this variation?

$A$ conductor of length $\ell$ with a circular cross-section is shown in the figure,carrying a current $i$. The radius of the cross-section varies linearly from $a$ to $b$. Assuming $(b - a) << \ell$,calculate the current density at a distance $x$ from the left end.