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  • A potential difference of 30 V is applied between the ends of a conductor of length 100 m and resistance  and uniform area of

A potential difference of 30 V is applied between the ends of a conductor of length 100 m and resistance 0.5\; \Omega and uniform area of cross-section. The total linear momentum of free electrons is -

Option: 1

3.4 \times 10^{-6} \mathrm{~kg} / \mathrm{s}


Option: 2

4.3 \times 10^{-6} \mathrm{~kg} / \mathrm{s}


Option: 3

3.4 \times 10^{-8} \mathrm{~kg} / \mathrm{s}


Option: 4

4.3 \times 10^{-8} \mathrm{~kg} / \mathrm{s}


Answers (1)

Current, \mathrm{I}=\frac{\mathrm{V}}{\mathrm{R}}=\frac{30}{0.5}=60 \mathrm{~A}

\therefore \quad Total\: momentum\: of\: all\: free \: e^{-} \mathrm{s}

and linear momentum of each e^{-} s, P=m v_\alpha

Total momentum of all free e¯s,

\begin{aligned} & \mathrm{P}=(\mathrm{nA} \ell)\left(m \mathrm{v}_\alpha\right) \\ & \text { But } \quad \mathrm{I}=\mathrm{neA} v_\alpha \text {, so } \mathrm{nA} v_\alpha=\frac{\mathrm{I}}{\mathrm{e}} \\ & \therefore \quad P=\frac{\mathrm{I} \ell \mathrm{m}}{\mathrm{e}}=\frac{60 \times 100 \times 9.1 \times 10^{-31}}{1.6 \times 10^{-19}} \\ & 3.4 \times 10^{-8} \mathrm{~kg} / \mathrm{s} \\ & \end{aligned}

Posted by

Sumit Saini

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