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A wire has a resistance of 2.5Omega at 2...

A wire has a resistance of `2.5Omega at 28^(@)C` and a resistance of `2.9Omega at 100^(@)C`. The temperature coefficient of resistivity of material of the wire is

A

`1.06xx10^(-3).^(@)C^(-1)`

B

`3.5xx10^(-2).^(@)C^(-1)`

C

`2.22xx10^(-3).^(@)C^(-1)`

D

`9.95xx10^(-2).^(@)C^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Here, `R_(1)=2.5Omega, T_(1)=28^(@)C`
`R_(2)=2.9Omega and T_(2)=100^(@)C`
`As, R_(2)=R_(1)(1+alpha(T_(2)-T_(1))]`
`therefore 2.9=0.591+alpha(100-28)]`
`(2.9)/(2.5)-1=alpha(72) or alpha=(1)/(2)xx(2.9-2.5)/(2.5)`
`=(1)/(72)xx(0.4)/(2.5)=2.22xx10^(-3).^(@)C^(-1)`
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