question_answer

A battery of internal resistance 4W is connected to the network of resistances as shown. In order to give the maximum power to the network, the value of R (in \[\Omega \]) should be                                              [IIT 1995]

A)            4/9

B)            8/9

C)            2

D)            18

Correct Answer: C

Solution :

                   The equivalent network is Clearly, the network of resistances is a balanced Wheatstone bridge. So \[{{R}_{AB}}\] is given by \[\frac{1}{{{R}_{AB}}}=\frac{1}{3R}+\frac{1}{6R}=\frac{2+1}{6R}=\frac{1}{2R}\] Þ \[{{R}_{AB}}=2R\] For maximum power transfer \[2R=4\Omega \]Þ \[R=\frac{4}{2}=2\Omega \]