Question

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

• A. $3.2W$
• B. $2.0W$
• C. $1.28W$
• D. $8/9W$

Answer 1

The correct option is B $2.0W$

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 $R=r+r=1+1=2\Omega$
Thus, $E+E=I(R+r+r)\Rightarrow I=\frac{2E}{R+2r}=\frac{2\times 2}{2+2}=1A$
Maximum power, $P=I^{2}R=1^2\times 2=2W$