Question

The velocity of charge carriers of current (about 1 ampere) in a metal under normal conditions is of the order of

• A. a fraction of mm/sec
• B. velocity of light
• C. several thousand metres/second
• D. a few hundred metres per second

Answer 1

The Correct Option is A

To understand the velocity of charge carriers in a metal under normal conditions when the current is about 1 ampere, we must explore the concept of drift velocity in conductors.

In a conductor, charge carriers (usually electrons) experience a small and average velocity known as the drift velocity due to the presence of an electric field. The drift velocity of electrons in a metallic conductor with current is given by the formula:

v_d = \frac{I}{nAe}, where:

• v_d is the drift velocity,
• I is the current (1 ampere in this case),
• n is the number of charge carriers per unit volume,
• A is the cross-sectional area of the conductor, and
• e is the charge of an electron.

In good conductors (like metals), despite a high density of charge carriers, the drift velocity is typically very small because of the small acceleration imparted due to the electric field.

For common metal conductors, this drift velocity is indeed very tiny, often about a fraction of a millimeter per second. This is due to the large number of electrons available per unit volume of the conductor and the relatively modest current value of 1 A compared to the massive number of available carriers.

Therefore, given the options, the correct answer is that the velocity of charge carriers is a fraction of mm/sec.

Let's briefly evaluate why the other options are incorrect:

• Velocity of light: The velocity of charge carriers is nowhere near the speed of light. Charge carriers move much slower due to frequent collisions within the lattice structure of metals.
• Several thousand metres/second: This would imply a far greater drift velocity than what is typical for metallic conductors under standard conditions.
• A few hundred metres per second: Even this would suggest a much higher drift velocity than practically observed in a typical metal conductor carrying a 1 ampere current.

In conclusion, the drift velocity of the order of a fraction of mm/sec aligns well with typical values observed for metals carrying a current of about 1 ampere.