A copper wire has diameter 0.5 mm and resistivity of

Question 6:

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

Solution:

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

∴ 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