Two resistances `R_1` and `R_2` are made of different materials. The temperature coefficient of the material of `R_1` is `alpha` and of the material of `R_2` is `-beta`. The resistance of the series combination of `R_1` and `R_2` will not change with temperature, if `R_1//R_2` equals.

Options

A. `alpha/beta`
B. `(alpha + beta)/(alpha - beta)`
C. `(alpha^(2) + beta^(2))/(alphabeta)`
D. `beta/alpha`

Answer

D

Explanation

`R = R_(1) + R_(2) = R_(1)(1 + alphat) + R_(2)[1 - betat]`
`rArr R = R_(1) + R_(2) + (R_(1)alphat - R_(2)betat)`
Since, R is independent of temperature-
`R_(1)alphat - R_(2)betat = 0`
`rArr R_(1)alpha = R_(2)beta rArr R_(1)/R_(2) = beta/alpha`