Question

What will be the resistivity of a metal wire of 2 m length and 0.6 mm in diameter, if the resistance of the wire is 50 Ω.

Answer 1

hello, dear tia! ^_^

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Here, given 

resistance = 50 Ω (R)
Length = 2 m ( l )
Diameter = 0.6 mm
∴ radius = 0.6/2 = 0.3 mm 

→ 0.3 mm =  3 x 10−⁴ m( converted to metres) 

we dun know abt resistivity,

Resistivity (ρ) =?

∴ area of cross section of wire = π r²

→ 3.14 x (3 x 10−⁴)²

→ = 2.826 x 10−⁹ m²

now, applying ρ = R X A / l

→ ρ = 50 Ω  x  2.826 x 10−⁹ m² / 2m

→ ρ  = 25 x 2.826 x 10−⁹ Ω  m

→ ρ = 70.65 x 10⁻⁹

→ ρ  = 7.065 x 10⁻⁸ Ω m

∴ resistivity ( ρ  ) = 7.065 x 10⁻⁸ Ω m

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for the one u thinks my answer is wrong.. see the attachment below.. -_-

hope it helps! ^_^ 

Answer 2

Hey!

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Resistance (R) = 50 Ω

Length of the wire ( l ) = 2 m

Diameter of the wire = 0.6 mm

Radius = 0.6 / 2 = 0.3 mm
= 3 × 10^-4 m

Resistivity ( ρ ) = ?

Area of cross sectional area of wire (A) = πr^2
= 3.14 ×( 3 × 10^-4)^2
= 2.826 × 10^9 m^2

We know,

ρ = RA / l

ρ = 50 × 2.826 × 10^-9 / 2

ρ = 25 × 2.826 × 10^-9

ρ = 70.65 × 10^-9 or 7.065 × 10^-8 Ω m

Resistivity of the wire is 7.065 × 10^-8 Ω m.
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Hope it helps...!!!