A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance, if its volume remains unchanged is
Question
A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance, if its volume remains unchanged is
Solution
The resistance (R) of a wire is given by the formula R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area.
If the volume remains constant, then the cross-sectional area (A) is inversely proportional to the length (L). This means that if the length increases by 0.5%, the cross-sectional area decreases by 0.5%.
The resistance is directly proportional to the length and inversely proportional to the area. So, if the length increases by 0.5% and the area decreases by 0.5%, the overall effect is that the resistance increases by 1%.
So, the percentage change in its electrical resistance is 1%.
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