the resistance of a wire is 60 at 25oc and 65 at

Question

The resistance of a wire is 60 ? at 25^oC and 65? at 75^oC. Find the resistance of wire at 0^oC and value of temperature co-efficient at 0^o C.

Ans:

Given R₂₅ = 60 ? and R₇₅ = 65 ?

R_t = R= (1 + α t)

Rt = R_O (1 + α_O t)

R₂₅= R_O (1 + α_O 25) -----------------(1)

R₇₅= R_O (1 + α_O 75) ------------------(2)

Divide (1) with (2)

(R₂₅/ R₇₅) = (R_O (1 + α_O 25))/(R_O (1 + α_O 75))

60/65 = (1 + α_O 25)/( 1 + α_O 75)

60 + 4500 α_O = 65 + 1625 α_O

2875 α_O = 5

α_O = 5 / 2875 = 0.001739 / ⁰C

R₂₅ = R_O (1 + 0.001739 X 25)

R_O  = 60 / 1.04348 = 57.49 ?