A 146 g mass of aluminum (Al) is formed into a right circular cylinder shaped so

Question

A 146 g mass of aluminum (Al) is formed into a right circular cylinder shaped so that its diameter equals its height.                                                                                                      (a) Find the resistance between the top and bottom faces of the cylinder at 20 °C. Use 2700 kg/m^3 as the density of Al and 2.82 × 10^8 · m as its resistivity. Answer in units of .                              (b) Find the resistance between opposite faces if the same mass of aluminum is formed into
a cube. Answer in units of .

Explanation / Answer

SOLUTION: Given the mass of the aluminium,    m=146x10-3 kg Density of the aluminium is,     =2.70x103 kg/m3 The specific resistance of the aluminium is,     =2.82 x10-8 /m Now the volume of the block is    V=m/       = 5.407 x 10-5 m3                                                    (a) Given the diameter is equal to its height,      d= h We know the formula for the volume of the cylinder in   terms of diameter is,        V=r2h         =(d/2)2d         =d3/4 From this,      d= (4V/)1/3        =(4 x 5.407 x 10-5m3 / 3.14)1/3         =0.0423 m We know the formula for the resistance is ,     R=L/A      =d/ (d2/4)      =4/d      =4(2.82*10-8/m) /(3.14)(0.0423 m)        = 8.49 x 10-7 ________________________________________________________ ________________________________________________________                              (b) In this case we have to calculate the resistance between the opposite faces of the aluminium cube. we know the formula for volume of the cube is,      V=L3    L=V1/3       =(5.407 x 10-5m3)1/3 From this the length of the cube is,      L= 0.039 m Now the resistance between the opposite faces of the cube is,      R=L/A       =L/L2        =/L        =(2.82*10-8/m)/(0.039 m)        =7.23 x10-7                  L=V1/3       =(5.407 x 10-5m3)1/3 From this the length of the cube is,      L= 0.039 m From this the length of the cube is,      L= 0.039 m Now the resistance between the opposite faces of the cube is,      R=L/A       =L/L2        =/L        =(2.82*10-8/m)/(0.039 m)        =7.23 x10-7        =/L        =(2.82*10-8/m)/(0.039 m)        =7.23 x10-7              

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