SOLUTION: A wire of 50 meters in length ans 2mm^2 in cross section has a resistance of 0.56 ohms. A 100m length of wire of the same material has a resistance of 2 ohms at the same temperatur

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Question 1086765: A wire of 50 meters in length ans 2mm^2 in cross section has a resistance of 0.56 ohms. A 100m length of wire of the same material has a resistance of 2 ohms at the same temperature. Find the diameter of the wire.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The resistance is proportional to the
volume of material
Convert meters to mm
+50%2A%28+1000%2F1+%29+=+50000+ mm
+50000%2A2+=+100000+ mm3
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Let +A+ = the area of the 2nd wire in mm2
+100%2A%28+1000%2F1+%29+=+100000+
+100000%2AA+ mm3 = volume of the 2nd wire
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+A+=+pi%2Ar%5E2+
+100000%2Api%2Ar%5E2+ mm3 = volume of the 2nd wire
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I can use a propotion:
+.56%2F2+=+100000+%2F+%28+100000%2Api%2Ar%5E2+%29+
+.28+=+1+%2F+%28+pi%2Ar%5E2+%29+
+pi%2Ar%5E2+=+1%2F.28+
+r%5E2+=+3.5714+%2F+3.1416+
+r%5E2+=+1.1368+
+r+=+1.0662+ mm
+d+=+2.1324+ mm
The diameter of the wire is 2.1324 mm
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check:
+.28+=+1+%2F+%28+pi%2Ar%5E2+%29+
+.28+=+1+%2F+%28+pi%2A1.1368+%29+
+.28+=+1%2F3.5714+
+.28+=+.280005+
close enough