The maximum power drawn out of the cell from a source is given by (where $r$ is internal resistance)
Medium
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$i = \frac{E}{{r + R}}$ $ \Rightarrow $ $P = {i^2}\,R$ $ \Rightarrow $ $P = \frac{{{E^2}R}}{{{{(r + R)}^2}}}$
Power is maximum when $r = R$ $ \Rightarrow $ ${P_{\max }} = {E^2}/4r$
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