Example from Physics, 19.4 Electric Power

Boot Warmers

To warm your boots on cold days, you decide to sew a circuit with some resistors into the insole of your boots. You want 10 W of heat output from the resistors in each insole, and you want to run them from two 9-V batteries (connected in series). What total resistance should you put in each insole?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We know the desired power and the voltage (18 V, because we have two 9-V batteries connected in series), so we can use the equation $P = V^{2} / R$ to find the requisite resistance.
Solution
Solving $P = V^{2} / R$ for the resistance and inserting the given voltage and power, we obtain

$\begin{matrix} P & = & \frac{V^{2}}{R} \\ R & = & \frac{V^{2}}{P} = \frac{{(18 V)}^{2}}{10 W} = 32 Ω. \end{matrix}$
19.52

Thus, the total resistance in each insole should be 32 $Ω.$

0 of 2 steps open

How did it go?

Strategy

Solution