Question

A wire is gradually stretched to make it 100% longer. Its resistance will increase by:

• A. 100%
• B. 200%
• C. 300%
• D. 400%

Hint:

Volume stays constant, so doubling the length halves the area. Then R = rho l / A becomes 4 times.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Stretching a wire changes its length and its cross-section, but the volume of the metal stays the same. The resistance is \(R = \dfrac{\rho l}{A}\).

Step 2: Key Formula or Approach:
Volume is constant, so \(A l = A' l'\). A wire made 100% longer has \(l' = 2l\).

Step 3: Find the new area:
\[ A' = \frac{A l}{l'} = \frac{A l}{2l} = \frac{A}{2} \]

Step 4: Find the new resistance:
\[ R' = \frac{\rho l'}{A'} = \frac{\rho (2l)}{A/2} = 4\,\frac{\rho l}{A} = 4R \]
The resistance becomes 4 times the old value. The increase is \(4R - R = 3R\).

Step 5: Percentage increase:
\[ \frac{R' - R}{R}\times 100 = \frac{3R}{R}\times 100 = 300\% \]

Step 6: Check the options:
100% would be right only if the length doubled and the area stayed the same, which cannot happen for a stretched wire.
200% corresponds to \(R' = 3R\) and 400% corresponds to \(R' = 5R\). Neither matches \(R' = 4R\). So option (C) is correct.

Final Answer:
The resistance becomes four times the original, so it rises by 300%. This is option (C). \[ \boxed{300\%} \]