Question

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

• A. $4/9$
• B. $2$
• C. $8/3$
• D. $18$

Answer 1

The correct option is B $2$

The given circuit is a balanced Wheatstone bridge. [Fig. 1]

No current will flow across $6R$ o the side $CD$. [Fig. 2]

$\therefore$ The equivalent circuit is:- [Fig. 3]

For maximum power net external resistance=Total internal resistance

$\therefore (3R\parallel 6R)\Omega =4\Omega$

$⟹\frac{3R\times 6R}{3R+6R}\Omega =4\Omega$

$⟹R=2\Omega$