Question

A copper wire has diameter 0.5mm and resistivity of 1.6.10 m what will be the length of this wire to make it's resistance 10? how much does the resistance change if the diameter is doubled​

Answer 1

Given, diameter, d=0.5 mm    resistivity, ρ=1.6×10−8 Ωm

Resistance, R=10 Ω

Let the length of wire be l.

     A=πd2/4

   R=ρl/A

        =πd2/4ρl

⟹l=4ρRπd2

 l=4×1.6×10−810×3.14×(0.5×10−3)2  l=122 m

R∝1/d2

If the diameter is doubled, resistance will be one-fourth.

Hence, new resistance =2.5Ω : answer