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Q.

A current of 1.0 A exists in a copper wire of cross-section $1.0 {mm}^{2}$ .Assuming one free electron per atom, the drift speed of the free electrons in the wire is _______ (The density of copper is $9000 kg m^{- 3}$ )

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a

0.074 {mms}^{- 1}

b

0.74 {mms}^{- 1}

c

74 {mms}^{- 1}

d

7.4 {mms}^{- 1}

answer is D.

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Detailed Solution

6 \times 10^{23}

Copper atoms have mass of 63.5 g and there is one conduction electron per atom

so no. of electrons per unit volume is

$n = \frac{6 \times 10^{23}}{63.5} \times 9 \times 10^{3}$

$n = 8.5 \times 10^{28} m^{- 3}$

$∴ v = \frac{i}{nAq} = \frac{1}{8.5 \times 10^{28} \times 10^{- 6} \times 1.6 \times 10^{- 19}}$

$= 0.000074 m/s$

$= 0 .074 mm/s$

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A current of 1.0 A exists in a copper wire of cross-section 1.0 mm2 .Assuming one free electron per atom, the drift speed of the free electrons in the wire is _______ (The density of copper is 9000 kg m−3 )