The length of a metallic wire is increased by 20 % and its area of cross section is reduced by 4 %. The percentage change in resistance of the metallic wire is __________.

Solution

Physics sir · 3 steps

Write R = ρ L/A for the new wire and take the exact ratio. Do not just add the percentages.

1. Resistance formula. For a wire, R = ρ L/A. The material is the same, so the resistivity ρ does not change. Only L and A change.
2. New dimensions. A 20% increase in length gives L' = 1.2L. A 4% reduction in area gives A' = 0.96A.

   R'/R = L'/L × A/A' = 1.2/0.96 = 1.25

3. So. R' = 1.25R, so the resistance increases by 25%.

The common slip: 24. Adding the percentages as 20 + 4 gives 24, not 25. That shortcut only works for small changes, and 20% is too large for it.

The idea to keep. When a change in a quantity is as large as 20%, work with exact ratios like 1.2/0.96. Adding percentages only works for very small changes.

Answer from the NTA final answer key. Solution by PrepWiser.