The resistance of a metal wire of length 1 m is 25 Ω at 20∘ Celsius. If the diameter of the wire is 0.3 mm, then the resistivity of the wire at that temperature is
The correct option is D. 1.76×10−6 Ωm.
Given: Length of metal wire, l=1 m
Diameter of the wire, d=0.3 mm
Radius r=0.32=0.15 mm=0.15×10−3 m
Resistance of the metal, R=25 Ω
Area of the wire A=πr2=π×(0.15×10−3)2
We know that Resistance, R=ρlA
where ρ is the resistivity of the wire.
⇒ ρ=RAl=25×π×(0.15×10−3)21=1.76×10−6 Ωm.