First slide

Drift velocity

Question

Assume that each atom of copper contributes one free electron, If the current flowing through a copper wire of 1 mm diameter is 1.1 A, the drift velocity of electrons will be [density of Cu = 9gcm ^-3, At. wt. of Cu = 63)

Difficult

A

0.3 mm/s
B

0.5 mm/s
C

O .1 mm/s
D

0.2 mm/s

Solution

The number of atoms in 63g of copper is equal to Avogadro's number = 6 .0 x 10²³
Volume of 63g copper $\frac{63}{density} = \frac{63}{9} = 7 {cm}^{3}$
$\begin{array}{l} ∴ n = \frac{6 \cdot 02 \times 10^{23}}{7} per {cm}^{3} \\ = (6 \cdot 02 \times 10^{29} / 7) per m^{3} \end{array}$
$A = π r^{2} = π {(0 \cdot 5 \times 10^{- 3})}^{2} m^{2}$
The drift velocity, $v_{d} = i / (neA)$
$\begin{array}{l} ∴ v_{d} = [\frac{1 \cdot 1}{(6 \cdot 02 \times 10^{29} / 7) \times (1 \cdot 6 \times 10^{- 19}) \times π {(0 \cdot 5 \times 10^{- 3})}^{2}}] \\ = 0 \cdot 1 \times 10^{- 3} m / s = 0 \cdot 1 mm / s \end{array}$

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