Question

resistance of a metal wire of length 5 m is 100 ohm if the area of cross section of the wire is 3 ×10^7 m^2 equal calculate the resistivity of the metal

Answer 1

Theoretically Given : resistance of a metal wire of length 5 m is 100 ohm if the area of cross section of the wire is 3 ×10^7 m^2 ,

Solution :

Formula :  R = þ × length/Cross section area

We have ,  Resistance, Length and Area has been given.

↪  Resistance = 100 Ω,

↪ Cross section area = 3 × 10⁻⁷ m²

↪  Length = 5 m

↪ 100 = þ × 5  ÷  ( 3 × 10⁻⁷ )

↪ 100( 3 × 10⁻⁷ )  ÷ 5 = þ

↪ 20 × 3 × 10⁻⁷ = þ

↪ 6 × 10⁻⁷⁺¹  = þ

↪ 6 × 10⁻⁶ Ω  = þ

Therefore, Required Resistivity  of resistance of metal is 6 × 10⁻⁶ Ω meters .

Answer 2

We know that , R = þ × length/Cross section area


Resistance = 100 Ω,

Cross section area = 3 × 10⁻⁷ m²

&
Length = 5 m

100 = þ × 5 / ( 3 × 10⁻⁷ )

þ = 100( 3 × 10⁻⁷ ) / 5

= 20 × 3 × 10⁻⁷

= 6 × 10⁻⁷⁺¹

= 6 × 10⁻⁶ Ω m


Thus, Resistivity of metal is 6 × 10⁻⁶ Ω m