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  4. The maximum power dissipated in an external resistance R, when connected to a cell of emf E and internal resistance r, will be

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Q. The maximum power dissipated in an external resistance R, when connected to a cell of emf E and internal resistance r, will be

J & K CETJ & K CET 2011Electromagnetic Induction

Solution:

Current $ \, \, \, \, \, \, \, \, i = \frac {E}{r + R}$
Power $ \, \, \, \, \, \, \, \, p = i^2 R$
$\Rightarrow \, \, \, \, p = \frac {E^2R}{(r + R)^2}$
Power will be maximum when r = R
$p_{max} = \frac {E^2}{4r}$