A copper wire has diameter 0.5 mm and resistivity of 1.6 × 10–8 Ω m. What will bethe length of this wire to make its resistance 10 Ω? How much does the resistancechange if the diameter is doubled?

Q.6:- A copper wire has diameter 0.5 mm and resistivity of 1.6 × 10–8 Ω m. What will bethe length of this wire to make its resistance 10 Ω? How much does the resistancechange if the diameter is doubled?

 

Answer:-

Area of cross-section of the wire, A =π (d/2) 2
Diameter= 0.5 mm = 0.0005 m
Resistance, R = 10 Ω
We know that
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∴ length of the wire = 122.72m
If the diameter of the wire is doubled, new diameter=2×0.5=1mm=0.001m

Let new resistance be Rʹ

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∴ the new resistance is 2.5 Ω