Question

What happens to the resistance of a wire if its length decreases?

Answer 1

If the length of a wire decreases, its resistance decreases as well. This is because the resistance of a wire is directly proportional to its length. The relationship between resistance (\(R\)) and length (\(L\)) is given by the formula:

\[
R = \rho \times \frac{L}{A}
\]

Where:

1. \(R\) is the resistance,
   

1. \(\rho\) is the resistivity of the material,
   

1. \(L\) is the length of the wire, and
   

1. \(A\) is the cross-sectional area of the wire.
   

So, if the length \(L\) decreases, the resistance \(R\) will also decrease, assuming the resistivity and cross-sectional area of the wire remain the same.