Resistance of wires in parallel

[Cataklyzm]

Homework Statement

My car has rear defrosters that are made of 13 wires embedded into the rear window. They can melt a thin layer of ice, roughly 2.25*10^-2 kg worth, in two minutes. These wires are all in parallel and are connected to the 12V battery of my car. Each is about 1.25m long and has a resistivity of 9.00*10^-8 Ω*m. What is the cross sectional area of each wire?

Homework Equations

R=ρL/A
Q=mL_f
P=Q/t

The Attempt at a Solution

So, I submitted this homework a while back. My instructor finally posted solutions. In the solutions, he has written R_total=$\frac{R^{12}}{13}$, which he uses throughout his solution. My question is: why would the resistances be multiplicative? My thought is it would look like this: R_total=$\frac{R}{13}$. Thank you for your time.

 

[CWatters]

I agree with you about R_total = R/13 if R is the resistance of each wire.

Perhaps post his whole solution?

 

[Cataklyzm]

Here's his solution:

 

[CWatters]

I still think you are right. It should be just the standard equation for resistors in parallel ..

Rtotal = 1/(1/R1 + 1/R2... +1/Rn)

If R1 = R2 = RN = R

then

Rtotal = 1/(13/R) = R/13

Simples.

 

[CWatters]

I haven't worked through the rest of the problem but I'm surprised using R¹³ gives a reasonable answer.

Time for bed here.

 

[Neelima]

My solution to problem.
Attachment

 

[berkeman]

Here's his solution:

This is an old thread, but it's interesting and instructive to find the error by the instructor...

Spoiler