If R1 and R2 are the resistance of a conductor at two temperatures t01C and t02C respectively, show that the temperature coefficient of resistance,α=R2−R1R1t2−R2t1
Given R1 and R2 are the resistance of a conductor at two temperatures t01C and t01C respectively.
We know that the resistance of a conductor varies with temperature as,
Rt=R0(1+t)
R0→ resistance at 0∘C,Rtto resistance at t∘C∝
∝→ temperature coefficient of resistance
We have R1=R0(1+t1)fort∘1C
And R2=R0(1+t2)fort∘2C
Taking ratio, =R2R1=R0(1+∝t2)R0(1∝t1)
We get, R2+R2∝t1=R1+R1∝t2
(Or)∝=R2−R1R1t2−R2t1