A certain heating element is made out of Nichrome wire and used with the standard voltage source of V=120 V. Immediately after the voltage is turned on, the current running through the element is measured at I1=1.28 A and its temperature at T1=25°C. As the heating element warms up and reaches its steady-state (operating) temperature, the current becomes I2=1.229 A.

Required:
Find this steady-state temperature T2.

Question

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moya1316 moya1316 · Answer 1 · 2021-07-19T04:06:33+02:00

Answer:

T₁ = 232.5 ºC

Explanation:

For this exercise let's start by finding the value of the resistance for the two currents, using Ohm's law

V = i R

R = V / i

i₀ = 1.28 A

R₀ = 120 / 1.28

R₀ = 93.75 ohm

i₁ = 1.229 A

R₁ = 120 / 1.229

R₁ = 97.64 or

Resistance in a metal is linear with temperature

ΔR = α R₀ ΔT

where the coefficient of thermal expansion for Nichrome is α=0.0002 C⁻¹

ΔT = [tex]\frac{\Delta R}{\alpha R_o}[/tex]

ΔT = [tex]\frac{97.64 \ -93.75}{ 0.00020 \ 93.75}[/tex]

ΔT = 2,075 10² C

ΔT = T₁-T₀ = 2,075 10²

T₁ = T₀ + 207.5

T₁ = 25+ 207.5

T₁ = 232.5 ºC