Answer to Question #71189 in Electric Circuits for Mr. Sandep Suvd

Question

Two resistors, made of different materials having temperature coefficient of resistance
a1=0.004 per degree Celcius and a2= 0.005 , are connected in parallel and consume equal power per degree celcius at 15 degree celcius. What is the ratio of power consumed in resistance R2 to that in R1 at 70 degree celcius? (Answer is 0.9615)

Answer 1

For t_1=15 °C

R_1=R_01 (1+α_1 t_1 ) and R_2=R_02 (1+α_2 t_1 ).

The ratio of power consumed in resistance R_2 to that in R_1 at 15 °C

P_(2,15°C)/P_(1,15°C) =U^2/R_2∶U^2/R_1 =U^2/R_2 ∙R_1/U^2 =R_1/R_2 =(R_01 (1+α_1 t_1 ))/(R_02 (1+α_2 t_1 ) ).

So

1=(R_01 (1+α_1 t_1 ))/(R_02 (1+α_2 t_1 ) ) → 1=(R_01 (1+0.004∙15))/(R_02 (1+0.005∙15) ) →1=0.98605 R_01/R_02 → R_02=0.98605〖∙R〗_01.

The ratio of power consumed in resistance R_2 to that in R_1 at 70 °C

P_(2,70°C)/P_(1,70°C) =(R_01 (1+0.004∙t_2 ))/(R_02 (1+0.005∙t_2 ) )=(R_01 (1+0.004∙70))/(0.98605〖∙R〗_01∙(1+0.005∙70) )=1.28/1.3311675=0.96156.

Answer. P_(2,70°C)/P_(1,70°C) =0.96156.