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Two resistances R1 and R2 are made of di...

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.

A

`(alpha)/(beta)`

B

`(alpha+ beta)/(alpha - beta)`

C

`(alpha^(2) + beta^(2) )/(2 alpha beta)`

D

`(beta)/(alpha)`

Text Solution

Verified by Experts

The correct Answer is:
D
`R_1 + R_2` = constant, `R_1` will increase, `R_2` decrease.
`R_1 alpha Delta T- R beta Delta T= 0 rArr R_(1) alpha Delta T= R_(2) beta Delta T`
`therefore (R_1)/(R_2) = (beta) / (alpha)`
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