Question

(a) At what temperature would the resistance of a copper conductot be double of its value of `0^(@)C`? (b) Does this same teperautre hold for alll copper conductors, regardless of shape and size? `[alpha_(c) = 4.0xx1-0^(-3).^(@)C^(-1)]`

Answer 1

a. The resistance of a wire varies with temperautre accroding
to the relation `R = R_(0) (1+alpha Delta theta). So`
`(R_(2))/(R_(1)) = (R_(0)[1+ alpha(t_2 - 0)])/(R_0[1+alpha(t_1 - 0)]) = ((1+alphat_(2)))/((1+ alphat_(2)))`
According to given problem
`R_(2) = 2R_(1)` and `t_(1) = 0`
So, `2 = 1 +alphat_(2), i.e., t_(2) = (1//alpha) = (1//4xx10^(-3)) = 250^(@)C`
b. As here `t_(2) (=1//alpha)` does not inculde dimension of the
conductor (L and S), it is valid for all copper conductors
whatever be their shape and size.