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  • A electric current of 16 A exists in a metal wire of cross section <img alt="\mathrm{10^{-6}\, m^{2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B10%5E%7B-6%7D%5C%2C%20m%5E%7B

A electric current of 16 A exists in a metal wire of cross section \mathrm{10^{-6}\, m^{2}} and length 1m. Assuming one free electrons per atom. The drift speed of the free electrons in the wire will be
( Density of metal \mathrm{=5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3,}  atomic weight \mathrm{=60} )

Option: 1

5 \times 10^{-3} \mathrm{~m} / \mathrm{s}


Option: 2

2 \times 10^{-3} \mathrm{~m} / \mathrm{s}


Option: 3

4 \times 10^{-3} \mathrm{~m} / \mathrm{s}


Option: 4

7.5 \times 10^{-3} \mathrm{~m} / \mathrm{s}


Answers (1)

best_answer

According to Avogadro's hypothesis
\mathrm{\frac{N}{N_A}=\frac{m}{M} \text { so } n=\frac{N}{V}=N_A \frac{m}{V M}=\frac{\rho N_A}{M}}

\mathrm{\text{Hence total number of atoms }\mathrm{n}=\frac{6 \times 10^{23} \times 5 \times 10^3}{60 \times 10^{-3}}}

\mathrm{=5 \times 10^{28} / \mathrm{m}^3}
As \mathrm{\mathrm{I}=\mathrm{n}_{\mathrm{e}}\, \mathrm{eA} \, \mathrm{v}_{\mathrm{d}}}

\mathrm{\text{Hence drift velocity }v_d=\frac{1}{n_e e A}}
\mathrm{v_d=\frac{16}{5 \times 10^{28} \times 1.6 \times 10^{-19} \times 10^{-6}}}
      \mathrm{=2 \times 10^{-3} \mathrm{~m} / \mathrm{s}}
 

Posted by

Deependra Verma

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