Question

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.

Answer 1

T₁ = 232.5 ºC

Step-by-step 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 =
`(\Delta R)/(\alpha R_o)`

ΔT =
`(97.64 \ -93.75)/( 0.00020 \ 93.75)`

ΔT = 2,075 10² C

ΔT = T₁-T₀ = 2,075 10²

T₁ = T₀ + 207.5

T₁ = 25+ 207.5

T₁ = 232.5 ºC