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

Options

A. a fraction of mm/s
B. velocity of light
C. several thousands m/s
D. a few hundred m/s

Answer

To determine the velocity of charge carriers in a metal under normal conditions for a current of about 1 A, we can follow these steps:

### Step 1: Understand the concept of current
Current (I) is defined as the rate of flow of charge (Q) through a conductor. Mathematically, it is expressed as:
\[ I = \frac{dQ}{dt} \]
where \( dQ \) is the charge flowing in time \( dt \).

### Step 2: Identify the charge carriers
In metals, the charge carriers are typically electrons. The movement of these electrons constitutes the electric current.

### Step 3: Relate current to charge carrier velocity
The current can also be expressed in terms of the charge carrier density (n), the charge of each carrier (e), the cross-sectional area of the conductor (A), and the drift velocity (v_d) of the charge carriers:
\[ I = n \cdot A \cdot e \cdot v_d \]
where:
- \( n \) = number of charge carriers per unit volume
- \( A \) = cross-sectional area of the conductor
- \( e \) = charge of an electron (approximately \( 1.6 \times 10^{-19} \) coulombs)
- \( v_d \) = drift velocity of the charge carriers

### Step 4: Estimate the drift velocity
For a typical metal under normal conditions, the drift velocity \( v_d \) is quite small. It is generally in the order of millimeters per second (mm/s).

### Step 5: Conclusion
Based on the above reasoning, the velocity of charge carriers (electrons) in a metal under normal conditions for a current of about 1 A is approximately a fraction of a millimeter per second.

### Final Answer:
The velocity of charge carriers of current (about 1 A) in a metal under normal conditions is of the order of a fraction of millimeter per second.

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