Question

On applying 10 V across the two ends of a 100 cm long copper wire, the average drift velocity (in cm s\(^{-1}\)) in the wire is (rounded off to two decimal places).............

Hint:

Drift velocity is a crucial parameter in electrical conductivity. It relates the flow of charge carriers to the applied electric field and can be calculated using fundamental material properties.

Answer 1

The drift velocity \( v_d \) can be calculated using the formula:
\[ v_d = \frac{I}{nAe} \] Where:
- \( I \) is the current,
- \( n \) is the electron density,
- \( A \) is the cross-sectional area of the wire, and
- \( e \) is the electron charge.
First, calculate the current \( I \) using Ohm’s law:
\[ I = \frac{V}{R} \] The resistance \( R \) of the wire is given by:
\[ R = \rho \frac{L}{A} \] Where:
- \( \rho = 1.67 \times 10^{-6} \, \Omega \, {cm} \) is the resistivity of copper,
- \( L = 100 \, {cm} \) is the length of the wire,
- \( A \) is the cross-sectional area of the wire (assumed to be 1 cm\(^2\) for simplicity).
Using \( n = 8.43 \times 10^{22} \, {cm}^{-3} \) for copper and \( e = 1.6 \times 10^{-19} \, {C} \), we can now calculate the drift velocity.
First, find the current:
\[ I = \frac{V}{R} = \frac{10}{1.67 \times 10^{-6} \times \frac{100}{1}} = 5.98 \, {A} \] Now, calculate the drift velocity:
\[ v_d = \frac{I}{nAe} = \frac{5.98}{8.43 \times 10^{22} \times 1 \times 1.6 \times 10^{-19}} = 4.47 \, {cm/s} \] Thus, the drift velocity is between 4.20 and 4.60 cm/s.