Question

A copper wire has a diameter of 0.5mm and resistivity of 1.6×10-5 Ωm. what will be the length

of this wire to make its resistance 10 Ω?

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Answer 1

★Given :-

• Resistivity ρ = 1.6 × 10⁻⁸ Ω m

• Resistance R = 10 Ω

• Diameter d = 0.5 mm

★To find:-

• Length of the wire.

★Solution:-

Given diameter = 0.5mm

Therefore,

Radius = Diameter/2

            =0.25mm

Converting units,

Radius r = 0.25 mm

               = 0.25 × 10⁻³ m

               = 2.5 × 10⁻⁴ m

Area = 6.25 π × 10⁻⁸ m²

Using the formula :-

✦R = ρ ( L ) / ( A )

 

Putting values :

➟ L = ( R × A ) / ρ

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

➟ L =  62.5 π / 1.6

➟ L = 122.72 m

Hence,the length of wire is 122.72m.

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