Homework Help: Resistance of wires in parallel

1. Jun 9, 2013

Cataklyzm

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
R=ρL/A
Q=mLf
P=Q/t

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

2. Jun 9, 2013

CWatters

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

Perhaps post his whole solution?

3. Jun 9, 2013

Cataklyzm

Here's his solution:

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4. Jun 9, 2013

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.

5. Jun 9, 2013

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.