The resistance of a conductor at `20 ^@C "is" 6.3 Omega and "at" 100^@C` it is `7.5 Omega` . Calculate the resistance of the conductor at `0^@C` and its temperature coefficient of resistance .

Explanation

Temperature dependence of resistance is given by `R= R_(0) (1 + alpha t)`. On substituting values we can write the following :
`6.3= R_(0) (1 + 20 alpha)` …(i)
`7.5 = R_(0) (1 + 100 alpha)` …(ii)
Divding equations (i) and (ii) we get
`(6.3)/(7.5) = (1 + 20 alpha)/(1 + 100 alpha) rArr 6.3 + 630 alpha = 7.5 + 150 alpha`
`rArr 480 alpha = 1.2 rArr alpha = (1.2)/(480) = 0.0025" per " ""^(@)C`
On substituting calculated `alpha` in equation (i) we get
`R_(0) = (6.3)/(1 + 20 alpha) = (6.3)/(1 + 20 xx 0.0025) = 6 Omega`