1) A car's rear window defroster uses $n=15$ strips of resistive wire in a parallel arrangement. If the total resistance is 1.4 ohms, what is the resistance of one wire?
Solution: I rearranged the formula and got the following answer $$ R= nR_{T} = (15)(1.4 \Omega) = 21 \Omega .$$
2) Question : What is the total power dissipated in the defroster if 12 V is applied to it?
Relevant equations:
$$ R_{T} = \frac {R}{n} $$ $$ P = \frac{V^2}{R} $$
The attempt at a solution:
To get the total power dissipated I assumed I would use the formula $$ P = \frac{V^2}{R} = \frac{12^2}{1.4 \Omega} = 102W $$
I was wrong though, the answer is 6.86 W in the answers section of the book.
$$ P = \frac{V^2}{R} = \frac{12^2}{21 \Omega} = 6.86 W $$
What I'm guessing is they used the resistance value of one wire (21 ohms) for the resistance. My question is, why did they use the resistance of one wire and not the total resistance of the wires? Especially since they were asking for the total power dissipated?
