Question

A copper wire has diameter 0.5mm and resistivity 1.6x10^-8ohm m what will be the length of this wire to make its resistance 10ohm

Answer 1

Given,
diameter of copper wire = 0.5mm = 5 × 10-⁴ m
resistivity = 1.6 × 10^-8 ohm.m
resistance = 10 ohm
Length = ?
we know,
R = dL/A
where R , d , L and A are resistance , resistivity , length and cross section area.

10 = 1.6 × 10^-8 × L/(πr²)
L = 10 × 3.14 × (2.5 × 10^-4)² × 10^8/1.6
L = 10× 3.14 × 6.25/1.6
L = 122.656 m

Answer 2

Answer:

122.72 m

Explanation:

Given :

Resistivity ρ = 1.6 × 10⁻⁸ Ω m

Resistance R = 10 Ω

Diameter d = 0.5 mm

= > Radius r = 0.25 mm = 0.25 × 10⁻³ m = 2.5 × 10⁻⁴ m

= > Area A = 6.25 π × 10⁻⁸ m²

We are asked to find length L :

We know :

R = ρ ( L ) / ( A )

= > L = ( R × A ) / ρ

Putting values here we get :

= > L = ( 10 × 6.25 π × 10⁻⁸ ) / 1.6 × 10⁻⁸  m

= > L =  62.5 π / 1.6

= > L = 122.72 m

Hence we get required answer!