Sapling Learning | (0-m1 6.30 x107 | Metal Your professor gives you a summer job

Question

Sapling Learning | (0-m1 6.30 x107 | Metal 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 4.07 mm and a length of 5.07 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. Silver Copper 5.69 x 10 Aluminum 3.50 x 10 Tungsten1.82 x107 Tin Titanium 180 x 10 8.70 x 10 Sample 1: R1 2160 Silver Aluminum Tin Copper Tungsten Titanium Sample 2: R2 = 68.5 Sample 3: R3=448

Explanation / Answer

diameter=d=4.07 mm

length=l=5.07 cm

as we know, resistance=resistivity*length/area

==>resistivity=resistance*area/length

=resistance*pi*(diameter/2)^2/length

==>conductivity=1/resistivity

=length/(resistance*pi*(diameter/2)^2)

sample 1:

conductivity=5.07*0.01/(2160 *10^(-6)*pi*(4.07*0.001/2)^2)

=1.8*10^6

hence the sample is of titanium.

sample 2:

conductivity=5.07*0.01/(68.5 *10^(-6)*pi*(4.07*0.001/2)^2)

=5.689*10^7

hence the sample is of copper.

sample 3:

conductivity=5.07*0.01/(448 *10^(-6)*pi*(4.07*0.001/2)^2)

=8.6986*10^6

hence the sample is of tin

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