A toaster uses a Nichrome heating wire. When the toaster is turned on at 20°C, the initial current is 1.50 A. A few seconds later, the toaster warms up and the current has a value of 1.22 A. The average temperature coefficient of resistivity for Nichrome wire is 4.5 10-4 (C°)-1. What is the temperature of the heating wire?
The relative change in resistivity as the wire heats up is 1.50/1.22 = 1.2295. That is a 22.95% INCREASE.
(delta T)* coefficient of resistivity = 0.2295
delta T = 0.2295/4.5*10^-4 = 510 C
T = 510 + 23 = 533 C
R = V/i , V is constant here
V/i2 = V/i1 (T2-T1)k
i1 = i2 (T2 - 20) k
1.5 = 1.22 (T2 - 20)(4.5 * 10^-4)
15000 = 5.49 T2 - 110
You can get it from there
In answer to your followup questions: delta T is the increase in temperature. The 22.95% resistance increase was explained in my first calculation. 1.2295 is the inverse of the current decrease factor, 1.22/1.50. Since I = V/R, the current varies inversely with the resistance at constant voltage
where are you getting 22.95% and what is delta T
Whoa - I forgot the definition. dr wls did it right !
drwls is correct. To get the percentage subtract 1.22 from 1.5, then divide by 1.22
To find the temperature of the heating wire, we can use the formula for the change in resistance with temperature:
ΔR = R₀ * α * ΔT
Where:
ΔR is the change in resistance,
R₀ is the initial resistance,
α is the average temperature coefficient of resistivity, and
ΔT is the change in temperature.
First, let's find the initial resistance of the heating wire. We know that the initial current is 1.50 A. To find the initial resistance, we can use Ohm's Law:
R₀ = V₀ / I₀
Where:
R₀ is the initial resistance,
V₀ is the initial voltage (which is not given), and
I₀ is the initial current.
Since we don't have the initial voltage, we'll need to make an assumption. Let's assume that the voltage is constant throughout the process, so we can use the initial voltage for R₀.
Now, let's find the change in resistance:
ΔR = R - R₀
Where R is the resistance when the current is 1.22 A.
Next, we can rearrange the formula to solve for ΔT:
ΔT = ΔR / (R₀ * α)
Finally, we can calculate the temperature of the heating wire using the formula:
T = T₀ + ΔT
Where:
T is the final temperature of the heating wire,
T₀ is the initial temperature (20°C), and
ΔT is the change in temperature.
By substituting the given values into the equations, we can find the temperature of the heating wire.