The rod given in the figure is made up of two different materials. Both have square cross sections of 3 mm side. The resistivity of the first material is 4 × 10 − 3 Ω . m and it is 25 cm long while second material has resistivity of 5 × 10 − 3 Ω . m and is of 70 cm long. What is the resistivity of rod between its ends?

Question

The rod given in the figure is made up of two different materials. Both have square cross sections of 3 mm side. The resistivity of the first material is   4  ×      10          −      3        Ω  .  m and it is 25 cm long while second material has resistivity of   5  ×      10          −      3        Ω  .  m and is of 70 cm long. What is the resistivity of rod between its ends?

Arthur Gillespie · Accepted Answer

Side of square cross section ,   a  =  3     m  m  =  3  ×      10          −      3           mCross section ,   A  =      a    2    =  (  3  ×      10          −      3            )    2    =  9  ×      10          −      6               m    2  Resistivity of first material ,       ρ    1    =  4  ×      10          −      3        Ω  .  mResistivity of second material ,       ρ    2    =  5  ×      10          −      3        Ω  .  mlength of first material ,       L    1    =  25     c  m  =  0.25     mlength of second material ,       L    2    =  70     c  m  =  0.7     mTo find = Resistivity of rod We can calculate the resistance due to the first material using :      R    1    =                    ρ        1                    L        1              A          R    1    =            4      ×              10                  −          3                    ×      0.25              9      ×              10                  −          6                            R    1    =  111.11     ΩSimilarly , we can calculate the resistance due to second material using :      R    2    =                    ρ        2                    L        2              A          R    2    =            5      ×              10                  −          3                    ×      0.7              9      ×              10                  −          6                            R    2    =  388.89     ΩSince they are connected in series , the total resistance is :  R  =      R    1    +      R    2      R  =  111.11  +  388.89    R  =  500     ΩHence, the total resistance of the rod is   500     Ω

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