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An electric wire is stretched to increase the strength by 25% by what percent will the resistance be increased and what will be increase in its resistivity |
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Answer» A ρ is resistivity of the material L is length in meters A is cross-sectional area in m² we know the resistance will go up, and I think it will go up by about 50%, but NEED the math. first find out how much the cross-sectional area changes. volume of a cylinder = cross-sectional area x h V = Ah initial volume V1 = A1h1 FINAL volume V2 = A2h2 volume does not change A1h1 = A2h2 A1/A2 = h2/h1 = 1.25 so cross-sectional area will go down by 1.25 now resistance calculation initial resistance R1 = ρL1/A1 final resistance R2 = ρL2/A2 R2/R1 = ρL2/A2 / ρL1/A1 R2/R1 = (ρL2/A2) * (A1/ρL1) R2/R1 = (L2/L1) * (A1/A2) so the ratio is the product of the TWO R2/R1 = 1.25 * 1.25 R2/R1 = 1.56 resistance goes up by 56% |
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