An insulated extension cord is made of a 1.5-meter long copper rod with a diameter of 2.3 millimeters. (a) What is the resistance of the extension cord? (b) If an aluminum wire of the same length will be used instead of copper what should be the diameter of the aluminum wire to have the same resistance?

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Kaeden Bishop · Accepted Answer

Step 1: GivenLength of copper wire = Length of almunium wire: l = 1.5 mDiameter of copper rod:       d    c    =  2.3  m  m  =  2.3  ×      10          −      3           mStep 2: Formula Used and calculations(a )Resistance of wire having resistitvity   ρ, length l, and cross-sectional area A is given by-Resistance of wire   R  =  ρ      l    A    =  ρ            4      l              π              d        2            Resistivity of copper wire is       ρ    c    =  1.7  ×      10          −      8        Ω  mOn substituting the respected values in the above relation we getResistance of copper wire   R  =  1.7  ×      10          −      8                  4      ×      1.5              π      (      2.3      ×              10                  −          3                            )        2                =  6.14  ×      10          −      3        Ωb) From the question, the resistance of copper wire = resistance of an aluminum wireResistivity of aluminium wire is       ρ    a    =  2.8  ×      10          −      8        Ω  mResistance of Aluminium wire:   R  =      ρ    a              4      l              π              d        a        2            On substituting the respected values in the above relation we get  6.14  ×      10          −      3        =  2.8  ×      10          −      8                  4      ×      1.5              π              d        a        2              ⇒      d    a    2    =            2.8      ×              10                  −          8                    ×      6              π      ×      6.14      ×              10                  −          3                      =  8.71  ×      10          −      6      Taking square root both sides we get  ⇒ diameter of Aluminium wire:       d    a    =  2.95  ×      10          −      3        m  =  2.95     m  mResistance of copper wire is   6.14  ×      10          −      3           ΩDiameter of the Aluminium wire is 2.95 mm.

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