(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

By ohm's law, current I is given by
`I=(6V)/(6Omega)=1A`
but, `i=n eAv_(d)`
or `v_(d)=(i)/(n eA)`
On substituting the values
For `n=` number of electron/volumee `=(10^(29))/(m^(3))` length of circuit `=10cm` cross section
`=A=(1mm)^(2)`
`v_(d)=(1)/(10^(29)xx1.6xx10^(-19)xx10^(-6))`
`=(1)/(1.6)xx10^(-4)(m)/(s)` Therefore the energy absorbed in the form of KE is given by
`KE=(1)/(2)m_(e)v_(d)^(2)xxnAI`
`=(1)/(2)xx9.1xx10^(31)xx(1)/(2.56)xx10^(20)xx10^(8)xx10^(6)xx10^(1)`
`=2xx10^(-17)J`
(b). Power loss is given by
`P=I^(2)R=6xx1^(2)=6W=6(J)/(s)`
Since, `P=(E)/(t)`
Therefore, `E=Pxxt`
or `t=(E)/(P)=(2xx10^(-17))/(6)=10^(-17)s`