## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

The ratio of the total power delivered when the resistors are connected in parallel to the total power delivered when the resistors are connected in series is $~9.5$
We can find the equivalent resistance when the resistors are connected in parallel: $\frac{1}{R_{eq}} = \frac{1}{2.5~k\Omega} + \frac{1}{3.5~k\Omega} + \frac{1}{4.5~k\Omega}$ $\frac{1}{R_{eq}} = \frac{126}{315~k\Omega} + \frac{90}{315~k\Omega} + \frac{70}{315~k\Omega}$ $\frac{1}{R_{eq}} = \frac{286}{315~k\Omega}$ $R_{eq} = \frac{315~k\Omega}{286}$ $R_{eq} = 1101.4~\Omega$ We can find the total power delivered: $P = \frac{V^2}{R_{eq}} = \frac{(100~V)^2}{1101.4~\Omega} = 9.0794~W$ We can find the equivalent resistance when the resistors are connected in series: $R_{eq} = 2.5~k\Omega + 3.5~k\Omega + 4.5~k\Omega$ $R_{eq} = 10.5~k\Omega$ We can find the total power delivered: $P = \frac{V^2}{R_{eq}} = \frac{(100~V)^2}{10,500~\Omega} = 0.9524~W$ We can find the ratio of the total power delivered: $\frac{9.0794~W}{0.9524~W} = 9.5$ The ratio of the total power delivered when the resistors are connected in parallel to the total power delivered when the resistors are connected in series is $~9.5$