Question

Two resistance R1 and R2 are made of different materials. The temperature coefficient of the material of R1 is alpha and of the material of R2 is -beta . The resistance of the series combination R1 and R2 will not change with temperature then ratio of resistance of two wire at 0 degree celcius will be

Answer 1

initial equivalent resistance of R1 and R2 = R1 + R2 ......(1)

we know, relation between resistance and temperature is given by,

R = R0[1 + a∆T]

where R0 is initial resistance and R is the resistance after increasing temperature ∆T and a is coefficient of the material.

now temperature is increased to T °C

then, change in equivalent resistance = R1(1 + αT) + R2[1 + (-β)T]

= R1 + R2 + (R1α -R2β)T

a/c to question,

equivalent resistance won't change with temperature.

so, R1 + R2 = R1 + R2 + (R1α -R2β)T

or, (R1α - R2β)T = 0

or, R1/R2 = β/α

hence, ratio of their resistances is β/α