Question

Resistance of a wire is \( 8\Omega \). It is drawn in such a way that it experiences a longitudinal strain of \( 400% \). The final resistance of the wire is:

• A. \( 100\Omega \)
• B. \( 200\Omega \)
• C. \( 300\Omega \)
• D. \( 400\Omega \)

Hint:

When a wire is stretched uniformly, its resistance changes as \( R' = R (1 + \text{strain})^2 \), where strain is the percentage increase in length.

Answer 1

The Correct Option is B

Step 1: Understanding the Relation Between Resistance and Strain
When a wire is stretched, its resistance changes according to the formula:
\[ R' = R \times (1 + \text{strain})^2 \] Given that the longitudinal strain is \( 400% \) (or \( 4 \)), the length of the wire increases by a factor of \( 1 + 4 = 5 \). The resistance of a wire is given by: \[ R' = R \times (5^2) \] Step 2: Substituting the Given Values \[ R' = 8 \times 25 = 200\Omega \] Step 3: Conclusion
Thus, the final resistance of the wire is \( \mathbf{200\Omega} \).