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 Definition of Current
Current (I) is defined as the flow of electric charge (Q) per unit time (t). Mathematically, it can be expressed as:
\[ I = \frac{dQ}{dt} \]
Where:
- \( I \) is the current in amperes (A),
- \( dQ \) is the charge in coulombs (C),
- \( dt \) is the time in seconds (s).

### Step 2: 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 (q), and the drift velocity (v_d) of the carriers:
\[ I = n \cdot A \cdot q \cdot v_d \]
Where:
- \( n \) is the number of charge carriers per unit volume (m^-3),
- \( A \) is the cross-sectional area of the conductor (m^2),
- \( q \) is the charge of each carrier (for electrons, \( q \approx 1.6 \times 10^{-19} \) C),
- \( v_d \) is the drift velocity of the charge carriers (m/s).

### Step 3: Estimate Parameters for Normal Conditions
Under normal conditions (room temperature), the density of charge carriers in metals (like copper) is typically around \( 10^{28} \) carriers/m³.

### Step 4: Calculate Drift Velocity
Assuming a typical cross-sectional area (A) of 1 mm² (which is \( 1 \times 10^{-6} \) m²), we can rearrange the formula to solve for drift velocity \( v_d \):
\[ v_d = \frac{I}{n \cdot A \cdot q} \]

Substituting the values:
- \( I = 1 \) A,
- \( n \approx 10^{28} \) carriers/m³,
- \( A = 1 \times 10^{-6} \) m²,
- \( q \approx 1.6 \times 10^{-19} \) C.

We get:
\[ v_d = \frac{1}{(10^{28}) \cdot (1 \times 10^{-6}) \cdot (1.6 \times 10^{-19})} \]

Calculating this gives:
\[ v_d = \frac{1}{1.6 \times 10^{3}} \approx 6.25 \times 10^{-4} \text{ m/s} \]
or approximately \( 0.625 \) mm/s.

### Step 5: Conclusion
Thus, the velocity of charge carriers in a metal under normal conditions for a current of about 1 A is of the order of 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 \( 0.625 \) mm/s.

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