A 20-W platinum wire at 20 $\degree$C with a temperature coefficient of resistivity of 3.9 x 10^-3 ( $\degree$C)^-1 will have what resistance at 100 $\degree$C? A)14 W B)20 W C)26 W D)28 W

Question

Quizplus · Accepted Answer

To solve this problem, we can use the formula for the temperature dependence of resistance:

R(T2) = R(T1) [1 + αΔT]

Where:
R(T1) is the resistance at temperature T1
α is the temperature coefficient of resistivity
ΔT is the change in temperature (T2 - T1)
R(T2) is the resistance at temperature T2

We can plug in the given values:

R(T1) = 20 W
α = 3.9 x 10^-3 /°C
ΔT = 100°C - 20°C = 80°C

R(T2) = 20 W [1 + (3.9 x 10^-3 /°C) x 80°C]

R(T2) = 20 W x 1.312

R(T2) = 26.24 W

Therefore, the resistance of the platinum wire at 100°F will be 26.24 W. The best choice is C.

A 20-W Platinum Wire at 20 °\degree° C with a Temperature Coefficient of Resistivity of 3

A 20-W Platinum Wire at 20 $\degree$ C with a Temperature Coefficient of Resistivity of 3