(A) Consider circuit in 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 `RI^(2)` per second tot he thermal energy. What time scale would number associate with energy in problem (a)? `n=` number of electron/volume`=(10^(29))/(m^(3))` length of circuit`=10cm`, cross-section `A=(1mm)^(2)`

Explanation

(a) current `I = (V)/(R) = (6V)/(6 Omega) = 1A`, driff velocity `v_(d) = (I)/(nA e) = (1)/(10^(29) xx (10^(-4)) xx (1.6 xx 10^(-19)) = (1)/(1.6) xx 10^(-4) m//s` No of electron in the wire `= nAI`
KE of all the electron `= (1)/(2) m_(e) u_(d)^(2) xx nAI = (1)/(2) xx (9.1 xx 10^(-31)) xx ((1)/(16) xx 10^(-4))^(2) xx 10^(29) xx(10^(-4)) xx 10^(-1)`
`= 2 xx 10^(-17) J`
(b) power loss `= I^(2) xx 6 = 6 J//s`
All the `KE` of electron would be lost in time `= (2 xx 10^(-17)J)/(6 J//s) = 0.33 xx10^(-17) s ~~ 10^(-17) s`