A wire has a resistance of 21.0 ohms. It is melted down, and from the same volume of metal a new wire is made that is three times longer than the original wire. What is the resistance of the new wire?
The resistance of the new wire is (in terms of its length, area resistivity); R2 = pL2/A2 And the resistance of the original wire is; R1 = pL1/A1 The ratio is;(resistivity will cancel because its the same for both situations) R2/R1 = L2A1/L1A2 given L2 = 3L1 R2/R1 = 3A1/A2 To find the new cross-sectional area ,require the volumes to be equal; L2A2 = L1A1 3L1A2 = L1A1 A2 = (1/3)A1 Sub this into the R2/R1 equation to get; R2/R1 = 9 R2 = 9R1 = (9)(21) = 189 ohms
