A constant voltage is applied across a wire of constant length. How do...
Dependence of Drift Velocity on Cross-Sectional Area of Wire
When a constant voltage is applied across a wire of constant length, an electric field is produced in the wire. This electric field applies a force on the free electrons present in the wire, causing them to drift towards the positive end of the wire. The drift velocity of these electrons is dependent on several factors, including the cross-sectional area of the wire.
Inverse Relationship
The drift velocity of electrons in a wire is inversely proportional to the cross-sectional area of the wire. This means that as the cross-sectional area of the wire increases, the drift velocity of electrons decreases, and vice versa.
Explanation
The reason for this inverse relationship is that as the cross-sectional area of the wire increases, the number of free electrons in the wire also increases. This increased number of electrons means that there is less resistance to the flow of current, which leads to a decrease in the electric field and, consequently, a decrease in the drift velocity of electrons.
Conversely, as the cross-sectional area of the wire decreases, there are fewer free electrons in the wire, which increases the resistance to the flow of current. This increased resistance leads to a higher electric field and, consequently, a higher drift velocity of electrons.
Conclusion
The relationship between the drift velocity of electrons and the cross-sectional area of the wire is an important concept in understanding the behavior of electric currents. By understanding this relationship, we can design wires of the appropriate dimensions to achieve the desired level of current flow for a given application.