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  4. Two identical batteries each of e.m.f 2 V and internal resistance 1 Ω are available to produce heat in an external resitance by passing a current through it. The maximum power that can be developed across R using these batteries is

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Q. Two identical batteries each of e.m.f $2 \,V$ and internal resistance $1\, \Omega$ are available to produce heat in an external resitance by passing a current through it. The maximum power that can be developed across $R$ using these batteries is

AIPMTAIPMT 1990Current Electricity

Solution:

For maximum current, the two batteries should be connected in series. The current will be maximum when external resistance is equal to the total internal resistance of cells i.e. $2 \,\Omega$.
Hence power developed across the resistance $R$ will be
$I^{2} R=\left(\frac{2 E}{R+2 r}\right)^{2} R=\left(\frac{2 \times 2}{2+2}\right)^{2} \times 2=2 \,W$