Question

The resistance of a wire is \( R \) ohm. If it is melted and stretched to \( n \) times its original length, its new resistance will be

• A. \( nR \)
• B. \( \frac{R}{n} \)
• C. \( n^2 R \)
• D. \( \frac{R}{n^2} \)

Hint:

When a wire is stretched to \( n \) times its length, its resistance increases by \( n^2 \) times.

Answer 1

The Correct Option is C

We use the formula for resistance: \[ R = \rho \frac{L}{A} \] If a wire is stretched to \( n \) times its length, then: - \( L' = nL \)
- Volume remains constant \( \Rightarrow A' = \frac{A}{n} \) New resistance: \[ R' = \rho \frac{nL}{A/n} = \rho \frac{n^2 L}{A} = n^2 R \]