Electric current is due to the drift of electrons in

In a wire of circular cross-section with radius $r$,free electrons travel with a drift velocity $V$ when a current $I$ flows through the wire. What is the current in another wire of half the radius and of the same material when the drift velocity is $2V$?

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

$A$ cylindrical conductor of length $2 \ m$ and area of cross-section $0.2 \ mm^{2}$ carries an electric current of $1.6 \ A$ when its ends are connected to a $2 \ V$ battery. Mobility of electrons in the conductor is $\alpha \times 10^{-3} \ m^{2}/V \cdot s$. The value of $\alpha$ is: (electron concentration $n = 5 \times 10^{28} \ m^{-3}$ and electron charge $e = 1.6 \times 10^{-19} \ C$)

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 potential difference across a conducting wire of length $20 \ cm$ is $30 \ V$. If the electron mobility is $2 \times 10^{-6} \ m^2 \ V^{-1} \ s^{-1}$,then the drift velocity of the electrons is