Question

Calculate the resistance of a copper wire 1000metre long and 50mm diameter if the resistivity of a copper is 1.7*10-8

Answer 1

QUESTION :-

Calculate the resistance of a copper wire 1000 metre long and 50 mm diameter if the resistivity of  copper is 1.7 × 10 ⁻⁸ Ω m.

SOLUTION :-

GIVEN  -

length of the wire ( l ) = 1000 m

resistivity of copper = 1.7 × 10⁻⁸ Ω m

diameter of the wire = 50 mm  = 50 × 10 ⁻³ m

radius of the wire (r) = diameter / 2

                           =  50 × 10⁻³ / 2 m  

                           =  25 × 10 ⁻³ m

Area of cross- section of the wire (A) = π r²

               =  π ( 25 × 10⁻³ m )²

               =  3.14 × 625 × 10 ⁻⁶ m²

               = 1962. 5 × 10⁻⁶ m²

     Resistance = ρ l/A

where,

     

    ρ  = resistivity

    l = length

    A = Area of cross section

putting the given values in the above formula.....

      Resistance  =  ( 1.7 × 10⁻⁸ Ω m ) × 1000 m/  1962. 5 × 10⁻⁶ m²

→     Resistance = 17/ 1962.5 Ω

→     Resistance = 0.00866 Ω