Question

The restivity of copper is 1.7×10^-18 ohm m. 1- What length of copper wire of duameter 0.1 mm will jave a resistance of 34 ohm? 2- If another copper wire with the same length but of half tht diameter as of the first is taken then what will be the ratio of its resistance to that of the first one?

Answer 1

resistivity, ρ=1.7×10−8 ohm−mdiameter, d=0.1 mm=0.1×10−3 marea of cross section, A=πd24resistance, R=34 ohm(a )R=ρlAR=ρlπd2434=1.7×10−8×l3.14×(0.1×10−3)24/341.7×10−8×0.0314×10−64=ll=15.7 m(b) If diameter is half, d=0.1×10−32 mR'=1.7×10−8×15.73.14×(0.1×10−3)216/R'=136 ohmR'/R=136/34

R'/R=4/1