Assume that each atom of copper contributes one electron. If...

Assume that each atom of copper contributes one electron. If the current flowing through a copper wire of $1 \mathrm{~mm}$ diameter is $1.1 \mathrm{~A}$, the drift velocity of electrons will be (Density of $\mathrm{Cu}=9 \mathrm{~g} \mathrm{~cm}^{-3}$, at. wt. of $\mathrm{Cu}=63$ ) (a) $0.3 \mathrm{~mm} / \mathrm{s}$ (b) $0.5 \mathrm{~mm} / \mathrm{s}$ (c) $0.1 \mathrm{~mm} / \mathrm{s}$ (d) $0.2 \mathrm{~mm} / \mathrm{s}$

Assume that each atom of copper contributes one electron. If the current flowing through a copper wire of $1 \mathrm{~mm}$ diameter is $1.1 \mathrm{~A}$, the drift velocity of electrons will be (Density of $\mathrm{Cu}=9 \mathrm{~g} \mathrm{~cm}^{-3}$, at. wt. of $\mathrm{Cu}=63$ )
(a) $0.3 \mathrm{~mm} / \mathrm{s}$
(b) $0.5 \mathrm{~mm} / \mathrm{s}$
(c) $0.1 \mathrm{~mm} / \mathrm{s}$
(d) $0.2 \mathrm{~mm} / \mathrm{s}$

Key Concepts

Unit Conversion Considerations

Unit conversions are necessary when dealing with physical quantities expressed in different measurement systems. For example, converting density from g/cm³ to kg/m³ or ensuring that the diameter of a wire is converted into the appropriate unit before calculating the cross-sectional area is essential for maintaining consistency in the calculations.

Drift Velocity

Drift velocity is the average velocity at which charge carriers, such as electrons, move through a conductor under the influence of an electric field. It is typically much lower than the random thermal speeds of the electrons and is directly related to the current density and the number density of charge carriers.

Relationship Between Current and Drift Velocity

The current in a conductor is given by the equation I = n * A * v_d * e, where 'I' is the current, 'n' is the number density of charge carriers, 'A' is the cross-sectional area of the conductor, 'v_d' is the drift velocity, and 'e' is the elementary charge. This relationship allows one to solve for the drift velocity when the other parameters are known.

Electron Number Density in Metals

To determine the number of conduction electrons in a metal, one often uses the density of the material, its atomic weight, and Avogadro's number. Assuming each atom contributes one free electron, the electron number density can be calculated using the formula: n = (density * Avogadro's number) / atomic mass. This is a crucial step in linking the material properties to its electrical characteristics.

Cross-sectional Area of a Wire

The cross-sectional area of a wire is essential for determining current density and is calculated based on the geometry of the conductor. For a circular wire, the area is given by A = ?*(d/2)^2, where 'd' is the diameter. Correct computation of this area is critical for accurately applying the drift velocity formula.

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