A battery of internal resistance `4Omega` 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 `Omega` should be
.

Options

A. `4//9`
B. `8//9`
C. 2
D. 18

Answer

C

Explanation

(c ) The equivalent network is
Clearly, the network of resistance is a balanced Wheatstone bridge. So `R_(AB)` is given by
`(1)/(R_(AB)) = (1)/(3R) + (1)/(6R) = (2 + 1)/(6 R) = (1)/(2 R)`
`R_(AB) = 2R`
For maximum power transfer
`2R = 4 Omega implies R = (4)/(2) = 2 Omega`