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Question

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.

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Solution

(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


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