The ratio of the resistance of conductor at temperature `15^(@)C` to its resistance at temperature `37.5^(@)C` is 4 : 5. The temperature coefficient of resistance the conductor is :

Options

A. `1/25""^(@)C^(-1)`
B. `1/50""^(@)C^(-1)`
C. `1/80""^(@)C^(-1)`
D. `1/75""^(@)C^(-1)`

Answer

D

Explanation

The resistance at temperature t is
`" "R_(t)=R_(0)(1+alphat)`
`" "R._(t)=R_(0)(1+alphat.)`
`rArr" "4=1+15 alpha" …(1)"`
`" "5=1+37.5alpha" …(2)"`
`rArr" "4/5=(1+15alpha)/(1+37.5alpha)`
`rArr" "4(1+37.5alpha)=5(1+15alpha)`
`" "75alpha=1`
`rArr" "alpha=1/75""^(@)C^(-1)`