Question

Two identical cells each of emf $E$ and internal resistance $r$ are connected in parallel with an external resistance $R$. To get maximum power developed across $R$, the value of $R$ is

• A. R = r/2
• B. R = r
• C. R = r/3
• D. R = 2r

Answer 1

Answer: (A)

R = r/2

Answer 2

Equivalent resistance $R_{ eq }=\frac{r}{2}+R=\frac{r+2 R}{2}$
$\therefore I=\frac{2 E}{r+2 R}$
For maximum power consumption $I$ should be maximum so denominator is minimum. For this
$r+2 R=(\sqrt{r}-\sqrt{2 R})^{2}+2 \sqrt{r} \sqrt{2 R}$
$\Rightarrow \sqrt{r}-\sqrt{2 R}=0$
$\Rightarrow R=\frac{r}{2}$