Question

The relation between $R$ and $r$ for which the power consumed in the external part of the circuit is maximum.

• A. $R=r$
• B. $R=\frac{r}{2}$
• C. $R=2r$
• D. $R=1.5r$

Answer 1

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

Circuit can be simplified as:


From the above circuit we observed that the arrangement is similar to a balanced Wheatstone's network as $R\times 4R=2R\times 2R$.

So, resistance between $\text{P}$ and $\text{Q}$ can be removed without affecting the effective resistance of the combination.


This can be simplified to


They both are parallel, so their equivalent,

$R_{eq}=\frac{3R\times 6R}{3R+6R}=2R$

As we know that maximum power is transferred when external resistance is equal to internal resistance of the battery.

So, for maximum power transfer,

$2R=r$

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

Therefore, option $\left(B\right)$ is correct.