Q. Consider a wire of length 4m and cross-sectional area 1 mm^{2} carrying a current of 2A. If each cubic metre of the material contains 10^{29} free electrons, find the average time taken by an electron to cross the length of the wire.

(a)4.2 × 10^{4} s

(b)3.2 × 10^{5} s

(c)3.8 × 10^{5} s

(d)3.2 × 10^{4} 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 $