Question

The maximum power dissipated by external resistance $R$ by a cell of an external emf $E$ and internal resistance $r$ is $E^2/4R$ which is obtained for

• A. $R<r$
• B. $R>r$
• C. $R=r$
• D. any value of $R$

Answer 1

The correct option is C $R=r$

Power dissipated at $R=i^{2}R$

$P=\frac{E^2}{(r+R{)}^2}R$

$\frac{aP}{aR}=0\Rightarrow E^2\left[\frac{(r+R{)}^2-R\times 2(R+r)}{(r+R{)}^4}\right]=0$

$\Rightarrow r^2+R^2+2Rr=2R^2+2Rr$

$\Rightarrow r^2=R^2$ or $r=R$