An electric wire is stretched to increase its length by 25%.By what % will the resistance be increased and what will be increase in its resistivity?
Step 1, Given Increase in length = 25% Step 2, We know, As R = ρLA 25% increase in length means length is now L' = (L+25% of L) i.e., L+25L100 L' = 1.25L Decrease in area will be L′×A′ = L.A (Since volume remains same) 1.25L×A′ = L.A A′=11.25A A' = 0.8A Now, R=ρLA putting L' = 1.25L and A' = 0.8A R=ρ1.25L0.8A So new resistance R′=1.56(ρLA) or R' = 1.56R % inrease in resistance (1.56R−R)R×100 = 56% New resistance R' is 56% greater than old resistance R Therefore for a 25% increase in length, the percentage increase in resistance is 56%.