Question

When the length of the wire is doubled its resistivity becomes four times?

Answer 1

When the length of a wire is doubled, the resistance of the wire increases, but the resistivity of the wire does not change.

Here’s why:

1. Resistivity (denoted by ρ) is a property of the material itself. It depends on the material and its temperature, but it doesn't change with the length or cross-sectional area of the wire.
   

1. Resistance (R) of a wire is related to its resistivity by the formula:
   

   \[
   R = \rho \times \frac{L}{A}
   \]
   where:
   - \( R \) is the resistance,
   - \( \rho \) is the resistivity,
   - \( L \) is the length of the wire,
   - \( A \) is the cross-sectional area of the wire.

When you double the length (L) of the wire, the resistance doubles, because resistance is directly proportional to the length of the wire. However, the resistivity (ρ) remains unchanged as it’s a material property, not affected by the wire’s length.

So, to clarify:

1. If the length is doubled, the resistance doubles.
   

1. The resistivity remains the same.
   

Therefore, resistivity doesn't become four times when the length is doubled. The factor of four would apply if the area of the wire were doubled (since resistance is inversely proportional to area).