Question

A battery of internal resistance $4\Omega$ is connected to the network of resistances as shown in Fig. In order that the maximum power can be delivered to the network, the value of R in $\Omega$ should be

• A. $\frac{4}{9}$
• B. $2$
• C. $\frac{8}{3}$
• D. $18$

Answer 1

The correct option is B $2$

For the maximum power, external resistance (load resistance) is equal to internal resistance.
If we care fully see the external resistances will make a balanced Wheatstone bridge circuit as shown in figure. So no current pass through $6R$ and it will not working.
Total external resistance is: $R_{eq}=\frac{(R+3R)(2R+4R)}{(R+2R)+(2R+4R)}=2R$
Now, $2R=r=4\Rightarrow R=2\Omega$