Question

State whether the following statement is True or False.

A wire is stretched to double its length. Then its resistance become four times.

Answer 1

This statement is true.

Explanation:

When a wire is stretched to double its original length, its volume remains constant, assuming uniform stretching.

Since,

\[ V = AL \]

\[ A'L' = AL \]

Given \(L' = 2L\),

\[ A' = \frac{A}{2} \]

We know that,

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

Therefore, the new resistance is

\[ R' =\rho\frac{2L}{A/2} \]

\[ R' =4\rho\frac{L}{A} \]

\[ {R' = 4R}\]