Three equal resistors in series with an emf source dissipate 10 W. With the same emf source connected across the 3 equal resistors in parallel, what will be the power dissipated?

Let the three identical resistors have resistance $R$ and the source voltage be $V$.

In series: $R_{series} = 3R$. Power dissipated is $P_{series} = \frac{V^2}{3R} = 10\text{ W} \implies \frac{V^2}{R} = 30\text{ W}$.

In parallel: $R_{parallel} = \frac{R}{3}$. Power dissipated is $P_{parallel} = \frac{V^2}{R/3} = 3 \left(\frac{V^2}{R}\right) = 3 \times 30\text{ W} = 90\text{ W}$.

In general, $P_{parallel} = n^2 P_{series} = 3^2 \times 10\text{ W} = 90\text{ W}$.

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