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Physics Question on Current electricity

A current of 5A is passing through a metallic wire of cross-sectional area 4×10−6m24\times10^{-6}m^2 If the density of the charge carriers in the wire is 5 ? 1026m−310^{26}m^{-3}, the drift speed of the electrons will be [e = 1.602 ? 10−19C10^{-19}C]

A

1.56×10−2ms−11.56 \times 10^{-2}ms^{-1}

B

1.98?10−2ms−11.98 ?10^{-2}ms^{-1}

C

2.42?10−2ms−12.42 ?10^{-2}ms^{-1}

D

2.84?10−2ms−12.84 ?10^{-2}ms^{-1}

Answer

1.56×10−2ms−11.56 \times 10^{-2}ms^{-1}

Explanation

Solution

In a metal, conduction current is due to electrons given by
I=nAev
⇒\Rightarrow drift velocity, V=InAeV=\frac{I}{nAe}
⇒v=55?1026?4?10−6?1.602?10−19\Rightarrow v = \frac{5}{5 ? 10^{26}? 4?10^{-6}? 1.602? 10^{-19}}
=14?1.602?101=\frac{1}{4 ? 1.602? 10^1}
=10−16.408=1.56?10−2m/s=\frac{10^{-1}}{6.408}=1.56? 10^{-2}m/s