Heat and Thermal ExpansionHard
Question
Two conductors have the same resistance at 0oC but their temperature coefficients of resistance are α1 and α2. The respective temperature coefficients of their series and parallel combinations are nearly
Options
A.
B.
C.
D.
Solution
Let R0 be the initial resistance of both conductors
∴ At temperature q their resistance will be,
R1 = R0 (1 + α1θ) and R2 = R0 (1 + α2θ)
for, series combination, Rs = R1 + R2
R0s (1 + αsθ) = R0(1 + α1θ) + R0(1 + α2θ)
where Rs0 = R0 + R0 = 2R0
∴ 2R0 (1 + αsθ) = 2R0 + R0 θ (α1 + α2)
or
for parallel combination, Rp =
Rp0 (1 + αp θ) =
Where, Rp0
∴
as α1 and α2 are small quantities
∴ α1 α2 is negligible
or
[1 - (α1 + α2)θ]
as (α1 + α2)2 is negligible
∴
∴ At temperature q their resistance will be,
R1 = R0 (1 + α1θ) and R2 = R0 (1 + α2θ)
for, series combination, Rs = R1 + R2
R0s (1 + αsθ) = R0(1 + α1θ) + R0(1 + α2θ)
where Rs0 = R0 + R0 = 2R0
∴ 2R0 (1 + αsθ) = 2R0 + R0 θ (α1 + α2)
or
for parallel combination, Rp =
Rp0 (1 + αp θ) =
Where, Rp0
∴
as α1 and α2 are small quantities
∴ α1 α2 is negligible
or
[1 - (α1 + α2)θ]as (α1 + α2)2 is negligible
∴
Create a free account to view solution
View Solution FreeMore Heat and Thermal Expansion Questions
The thermo e.m.f. E in volts of a certain thermocouple is found to very with temperature difference θ in oC between...A thermodynamic system undergoes cyclic process ABCDA as shown figure. The work done by the system is : -...A glass rod measured with a zinc scale, both being at 30oC appears to be of length 100cm. If the scale shows correct rea...Two identical square rods of metal are end are welded end to end as shown in figure (a) 20 calories flows through it in ...The solar constant for the earth is ∑. The surface temperature of the sun is T K. The sun sub tends an angle θ...