1 Answer
When a wire is stretched, its resistance increases. This happens because of the relationship between the wire's length, cross-sectional area, and its resistance. Let's break it down step by step:
\[
R = \rho \times \frac{L}{A}
\]
Where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the wire,
- \( A \) is the cross-sectional area.
As the length \( L \) increases, the resistance \( R \) will also increase.
So, in summary:
Both of these effects (increased length and decreased area) contribute to a higher overall resistance when the wire is stretched.
- Length of the wire increases: When you stretch a wire, its length gets longer. According to the formula for resistance:
\[
R = \rho \times \frac{L}{A}
\]
Where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the wire,
- \( A \) is the cross-sectional area.
As the length \( L \) increases, the resistance \( R \) will also increase.
- Cross-sectional area decreases: When you stretch a wire, its volume remains constant. If you stretch it, the wire becomes thinner (its cross-sectional area \( A \) decreases). A smaller cross-sectional area increases the resistance as well, because the current has less room to flow through.
So, in summary:
- Longer wire = higher resistance.
- Thinner wire = higher resistance.
Both of these effects (increased length and decreased area) contribute to a higher overall resistance when the wire is stretched.