Question

A battery if internal resistance $4\Omega$ is connected to the network of resistances as shown. What must be the value of $R$ so that maximum power is delivered to the network?

• A. $4\Omega$
• B. $2\Omega$
• C. $1\Omega$
• D. $0.5\Omega$

Answer 1

The correct option is B $2\Omega$

External network is wheatstone bridge. Also it is balanced because, $\frac{R}{2R}=\frac{2R}{4R}$.

So we can remove the $6R$ resistance because current will not flow through it.



Both the resistance are in parallel, so equivalent resistance of the external netork, $R_{eq}=\frac{3R\times 6R}{3R+6R}=2R$.

For maximum power trasfer, external resistance should be equal to internal resistance of the battery.
So, $R_{eq}=r$
$\Rightarrow 2R=4$
$\therefore R=2\Omega$