question_answer

Five equal resistance, each of resistance R are connected as shown in figure below. A battery of V volt is connected between A and B. The current flowing in FC will be

A)  \[\frac{3V}{R}\]                                              

B)  \[\frac{V}{R}\]

C)  \[\frac{V}{2R}\]                                              

D)  \[\frac{2V}{R}\]

Correct Answer: C

Solution :

                 The effective figure can be given by From the wheat stone bridge balance, we get \[\frac{R}{R}=\frac{R}{R}=1\]      Hence, no current flows through the central resistance C. Thus, the effective resistance is equal to \[\frac{1}{{{R}_{eff}}}=\frac{1}{(R+R)}+\frac{1}{(R+R)}=\frac{1}{2R}+\frac{1}{2R}=\frac{1}{R}\] Hence,                  \[{{R}_{eff}}=R\] Now, the current \[I=\frac{V}{R},\]hence the current through FC would be equal to \[\frac{I}{2}=\frac{V}{2R}.\]