### 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 ΩWe know that

∴ 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

∴ the new resistance is 2.5 Ω