Question

A metal wire of cross-sectional area \(0.5\,\text{mm}^2\) and length \(100\,\text{m}\) is connected across a battery of e.m.f. \(2\,\text{V}\) and internal resistance \(1\,\Omega\). The density, atomic mass and electrical conductivity of the metal are \(6.35 \times 10^3\,\text{kg m}^{-3}\), \(63.5\,\text{gm/mole}\) and \(2 \times 10^8\,\text{mho m}^{-1}\), respectively. Assuming one conduction electron per atom of the metal, the drift velocity (in \(\text{mm s}^{-1}\)) of the electrons in the wire is:
(Take Avogadro’s number as \(6 \times 10^{23}\) and charge of the electron as \(1.6 \times 10^{-19}\,\text{C}\).)

• A. $0.052$
• B. $0.104$
• C. $0.208$
• D. $0.156$

Hint:

Remember to convert molar mass to kg/mole ($M = 0.0635\text{ kg/mole}$) to maintain SI unit consistency when using density in $\text{kg/m}^3$. This is a common source of decimal errors.

Answer 1

The Correct Option is C