Solve Nichrome Wire Resistivity Problem

In summary: The resistance of copper would be calculated as follows:Resistance= resistance x length/Area. Resistance measured in ohms of course.Resistance= 1.7 x 10^-7 x 0.08/0.8 = 3.2 ohms
  • #1
Sino87
4
0

Homework Statement


A toaster uses a Nichrome heating wire. When the toaster is turned on at 27 deg C, the initial current is 1.50A. A few seconds later, the toaster warms up and the current is now 1.30A. The avg. temp coefficient of resistivity for Nichrome wire is 4.5 x 10 ^ -4 (degree C) ^-1. What is the temperature of the heating wire?

Homework Equations



Nichrome(alloy) p=100 x 10^-8 ohm*m.
p = po [1 + alpha(T - To)]
To=20 deg C.
alpha=4.5x10^-4 (deg C)^-1
Io=1.50A
I=1.30A
T-?

The Attempt at a Solution



My attempt.

R = Ro [1 + alpha(T - To)]

R - Ro = alpha(T-To)

R=V/I

T= V(1/I - 1/Io)/alpha + 20

T = 20 + V(227.72)

V = (T-20)/227.92

T = 20 + (T-20/227.12) (227.12)

The answer is 360 deg C btw.
 
Last edited:
Physics news on Phys.org
  • #2
The voltage across the toaster must be constant, and the current changes (decreases) as the resistance increases with temperature. One knows the initial temperature and current, and final current, so use these to solve for the unknown temperature.

V = IR = I1R1 = I2R2, and then write R from R = po(1 + alpha(To-T)), where To = 20°C.
 
  • #3
R = po(1 + alpha(To-T))
i don't think that's right becuse po = RA/l
 
  • #4
Actually (I think you know what you have done wrong by now)...

R=R0( 1+ a(T-T0))

T= T0 + (R - R0 )/a
R = V/I
R0=V/I0
T= 20 + V(1/I - 1/I0)/a

what was the voltage?

T= 20 + V( 1/1.30 - 1/1.5)/ 4.5x10^-4=
T= 20 + V(227.92)

for 12 V we have plenty...

T= 20 + 12(227.92)=2760 C
 
  • #5
^Did you post on yahoo answers? Well anyways, no voltage was given and the answer is 360 degrees.
 
  • #6
yes i did post there...
 
  • #7
Ok lol. Yeah, I thought your posts was familiar. Thanks for the help, but the Voltage wasn't given in the problem. Your method totally makes sense, but when I solve for V and replug it into the original equation I get 20 deg C, when it should be 360 deg C.
 
Last edited:
  • #8
Given the following data on copper, how do i calculate the resistivity?

Relaxation time: 2.50e10-14s
Density: 8940Kgm-3
molar mass: 63.5g

is there an equation for it.
 
  • #9
i have a question on resistivity which i can't do, anyone please help me.
Question: Calculate the resistance of a rectangular strip of copper length 0.08m, thickness 15mm and width 0.80mm. The resistivity of of copper = 1.7 x 10^-7. Equations that are relevant:
Resistance= resitivity x length/Area. Resistance measured in ohms of course.
for a conductor with a circular cross section of diameter,d = pi(3.142) x d squared/4.
pleaseee help
 

Related to Solve Nichrome Wire Resistivity Problem

1. What is nichrome wire resistivity?

Nichrome wire resistivity is a measure of a material's ability to resist the flow of electric current. It is represented by the Greek letter ρ (rho) and is measured in ohm-meters (Ω•m).

2. How do I calculate the resistivity of nichrome wire?

The resistivity of nichrome wire can be calculated using the formula ρ = RA/L, where R is the resistance of the wire, A is the cross-sectional area, and L is the length of the wire.

3. How does temperature affect the resistivity of nichrome wire?

The resistivity of nichrome wire increases as temperature increases. This is due to the increased atomic vibrations within the wire, which leads to more collisions between electrons and atoms, hindering the flow of current.

4. What are the common applications of nichrome wire?

Nichrome wire is commonly used in heating elements, such as in toasters, hair dryers, and electric stoves. It is also used in electrical resistors and in the production of electrically heated thermocouples.

5. How can I use nichrome wire resistivity to design a heating element?

To design a heating element using nichrome wire, you will need to calculate the appropriate length and gauge of wire needed to reach the desired resistance. This can be done using the formula R = (ρL)/A, where R is the desired resistance, ρ is the resistivity of nichrome wire, L is the length of the wire, and A is the cross-sectional area.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
4K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
12
Views
523
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
20
Views
5K
  • Introductory Physics Homework Help
2
Replies
44
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
974
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
4K
  • Introductory Physics Homework Help
Replies
4
Views
1K
Back
Top