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A battery of ...

Question

A battery of $e m f E$ and internal resistance $r$ . The value of external resistance $R$ so that the power across external resistance is maximum:

A

r

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B

2 r

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C

\frac{r}{2}

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D

\frac{r}{4}

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Solution

The correct option is B $r$
$i = \frac{E}{(R + r)}$
$P$ across $R = i^{2} R = \frac{E^{2}}{(R + r)^{2}} \times R$
$\frac{d P}{d R} = 0$
$R = r$

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