A wire of 3 ohms resistance and 15 cm in length is stretched to 45 cm in length. Calculate the following:
i) New cross sectional area
ii) New resistance
iii) Resistivity.
Assume that wire has a uniform cross sectional area.
(i) Let the initial area be A
The volume will be the same in both conditions
Volume=A×Length
∴A(15)=A2(45)
---> new area A2=A(1545)=A3
New cross-sectional area = 1/3 of the initial area
(ii)
R=ρLA
New length is 3 times the initial length
The new area is 1/3 of the initial area
So new resistance R′=ρ(3LA3)=9(ρLA)=9R=9(3)=27Ω
(iii)
R=ρ(LA)
∴3=ρ(0.15A)
∴ρ=3A0.15
∴ρ=20A
where A is the area of the conductor