two resistances r1 and r2 are made of different materials the temperature coefficient of material of r1 is (alpha) - Physics - Electric Charges And Fields

Question

two resistances r1 and r2 are made of different materials the
temperature coefficient of material of r1 is (alpha) and of the
material of r2 is -beta the resistance of the series combination of
r1 and r2 will not change with temperature, then find the ratio of
r1 and r2

Krishan Yadav · Accepted Answer

Dear Student,

Resistance depends on temperature like

R' = Rref (1+α(T-Tref))    (R' = resistance at temperature T)In our caseR' for r1 resistance is given by R1' =r1 (1+α(T-Tref))R' for r2 resistance is given by R2' =r2 (1-β(T-Tref))In case of series connection we are given that R1' +R2'  =r1  + r2 r1 (1+α(T-Tref)) +r2 (1-β(T-Tref)) =r1  + r2 r1  + r2  +r1  α(T-Tref) -r2 β(T-Tref) =r1  + r2 r1  α(T-Tref) = r2 β(T-Tref)r1 r2  =βα
Regards

two resistances r1 and r2 are made of different materials. the temperature coefficient of material of r1 is (alpha) and of the material of r2 is -beta. the resistance of the series combination of r1 and r2 will not change with temperature, then find the ratio of r1 and r2.