Q. Consider a wire of length 4m and cross-sectional area 1 mm2 carrying a current of 2A. If each cubic metre of the material contains 1029 free electrons, find the average time taken by an electron to cross the length of the wire.
(a)4.2 × 104 s
(b)3.2 × 105 s
(c)3.8 × 105 s
(d)3.2 × 104 s
Ans: (d)
Sol:
drift velocity
$ \displaystyle v_d = \frac{I}{n e A} $
$ \displaystyle v_d = \frac{2}{10^{29}\times 1.6\times 10^{-19}\times 10^{-6}} $
$ \displaystyle v_d = \frac{2}{1.6 \times 10^4} $
Time taken by an electron to cross the length of the wire is
$ \displaystyle t = \frac{l}{v_d} $
$ \displaystyle t = \frac{4}{2/(1.6 \times 10^4)} $
$ \displaystyle t = \frac{4\times 1.6 \times 10^4}{2} $
$ \displaystyle = 3.2 \times 10^4 sec $