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  4. Two identical cells are first connected in series and then in parallel. The ratio of power consumed by them is

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Q. Two identical cells are first connected in series and then in parallel. The ratio of power consumed by them is

AMUAMU 2017

Solution:

Let emf of a cell $= \varepsilon $
and its internal resistance $= r$
Power consumed by any resistance $R$ is given by
$P = \frac{V^2}{R}$
For series combination,
$V = 2\varepsilon$ and $R = 2r$
$\therefore P_s = \frac{(2\varepsilon)^2}{2r} = \frac{2\varepsilon^2}{r}$
For parallel combination, $V = \varepsilon $ and $R = \frac{r}{2}$
$\therefore P_{p} = \frac{\varepsilon^{2}}{\frac{r}{2}} = \frac{2\varepsilon^{2}}{r} $
Hence, $\frac{P_{s}}{P_{p} } = \frac{2\varepsilon^{2}}{r} \times \frac{r}{2\varepsilon_{^{2}}} = \frac{1}{1}$