Question

Find the current flows through a copper wire of length 0.2 m, area of cross-section $1m{m}^2$ , when connected to a battery of 4V. Given that electron mobility is $4.5\times {10}^{-}6m^2{s}^{-}1$ and charge on an electron is $1.6\times {10}^{-19}C$ The number density of electron in copper wire is $8.5\times {10}^{2}8m^3$

Answer 1

Given that,

Length $l=0.2m$

Area $A=1m{m}^2$

Voltage $V=4v$

Electron mobility $\mu =4.5\times {10}^{-6}{m}^2/s$

Charge $e=1.6\times {10}^{-19}C$

Number density $n=8.5\times {10}^{-18}{m}^3$

We know that,

The current flows is

$I=neA{v}_d$

$I=neA\mu \frac{V}{l}$

$I=8.5\times {10}^{28}\times 1.6\times {10}^{-19}\times {10}^{-6}\times 4.5\times {10}^{-6}\times \frac{4}{0.2}$

$I=1224\times {10}^{-3}A$

$I=1.22A$

Hence, the current is $1.22A$