Question

A copper wire has diameter 0.5 mm and resistivity of 1.6×10^-8ohm m.
What will be the length of the wire to make its resistance 10 Ohm?
How much does the resistance change if the diameter is doubled?

Answer 1

Area of cross-section of the wire, A =? (d/2) 2  

Diameter= 0.5 mm = 0.0005 m  

Resistance, R = 10 ?

We know that  

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? length of the wire = 122.72m  

yaha If the diameter of the wire is doubled, new diameter=2�0.5=1mm=0.001m  

Let new resistance be R?  

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? the new resistance is 2.5 ?

Answer 2

Explanation:

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