Your professor gives you a summer job organizing his lab. On the first day you c

Question

Your professor gives you a summer job organizing his lab. On the first day you come across three identically shaped cylinders of metal, each having a diameter of 7.99 mm and a length of 3.39 cm. They appear to be made out of different metals, but they are not labeled! They are, however, packaged with a table of the conductivities of several metals. You locate a multimeter and use it to measure the electrical resistance of each cylinder. Using the measured resistances and the table of conductivities, identify the metal that each cylinder is composed of. Sample 1: R1 E 10.7 Aluminum Tungsten Tin Sample 2: R 19.3 AM2 Titanium Silver Sample 3: R3 376 Am Copper Metal or (Q m) Silver 6.30 x 107 Copper 5.69 x 107 Aluminum 3.50 x 10' Tungsten 1.82 x 10 Tin 8.70 x 106 Titanium 1.80 x 100

Explanation / Answer

Sample 1: R1 = 10.7

resistivity = R1 xA/L = 10.7X10^-6x(3.14x(0.00799/2)^2)/0.0339 = 1.5817X10^-8 ohm.m

so, conductivity = 1/1.5817x10^-8 =6.32x10^7 (ohm.m)^-1

so, the sample is SILVER

Sample 2: R2 = 19.3

resistivity = R1 xA/L =19.3X10^-6x(3.14x(0.00799/2)^2)/0.0339 = 2.853x10^-8 ohm.m

so, conductivity = 1/2.853x10^-8 = 3.50x10^7 (ohm.m)^-1

so, the sample is ALUMINUM

Sample 3: R3 = 376

resistivity = R1 xA/L =376x10^-6x(3.14x(0.00799/2)^2)/0.0339 = 0.5558 x10^-6

CONDUCTIVITY = 1/0.5558x10^-6 = 1.799x10^6 (ohm.m)^-1

so, the sample is Titanium

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