A wire with resistivity 1.8 xx 10^(-7) Omega m has a resistance of 0.45 Omega and a length of 2.0 m. What is the diameter of the wire in mm?

Shyla Odom

Shyla Odom

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2022-08-21

A wire with resistivity 1.8 × 10 7 Ω   m has a resistance of 0.45   Ω and a length of 2.0 m. What is the diameter of the wire in mm?

Answer & Explanation

Alyvia Marks

Alyvia Marks

Beginner2022-08-22Added 12 answers

Given data:
The given resistivity of wire is = 1.8 × 10 7 ohm-m
The value of resistance is R = 0.45 ohm
The given length of wire is l = 2.0 m
The expression for the cross-section area of a wire in terms of diameter d can be given as:
A = π ( d 2 ) 2
The expression for the resistance in terms of resistivity is,
R = ρ l A
Substitute the expression of the cross-section area, in an expression of resistance as:
R = ρ l π ( d 2 ) 2
Rearrange the expression for d.
d = ( 1.8 × 10 7 ) ( 2.0 ) ( 2 2 ) π ( 0.45 ) = 1.0 × 10 3   m = 1.0   m m

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