Question

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

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

Answer 1

The correct option is B $2$

This is a balanced wheatstone bridge.
$R_{eq}=\frac{(2R+R)(4R+2R)}{(2R+R)(4R+2R)}$
$=\frac{3R\times 6R}{9R}$ $=2R$
By maximum power transfer theorem, power transfer will be maximum when
Internal resistance$=$external resistance
$4\Omega =2R$
Or $R=2\Omega$
Hence, option $\left(b\right)$ is correct.