Question

Two cells each of electromotive force $E$ and internal resistance $r$ are concerned in parallel across the resistance $R$. The maximum energy given to the resistor per second if:

• A. $R=\frac{r}{2}$
• B. $R=r$
• C. $R=2r$
• D. $R=0$

Answer 1

The correct option is A $R=\frac{r}{2}$

$R_{eq}=\frac{r}{2}+R=\frac{r+2R}{2}$

$I=\frac{2E}{r+2R}$

For max. power consumption$.$ I should be max. so denominator should be min. for that

$r+2R={\left(\sqrt{r}-\sqrt{2R}\right)}^2+2\sqrt{r}\sqrt{2R}$

$\Rightarrow \sqrt{r}-\sqrt{2R}=0$

$\Rightarrow R=\frac{r}{2}$

Hence,

option $\left(A\right)$ is correct answer.