question_answer

Each of the resistance in the network shown in figure is equal to R. Find the equivalent resistance between two terminals A and B.

A) \[R\]                                     

B)        \[5R\]

C)        \[2R\]                                   

D)        \[\frac{2}{3}R\]

Correct Answer: A

Solution :

Simplified form of the circuit is shown below. The simplified circuit is balanced Wheatstones bridge, so the resistance in arm DC remains unaffected. Resistance of upper arms             \[{{R}_{U}}=R+R=2R\] Resistance of lower arms \[{{R}_{L}}=R+R=2R\] Net resistance of the circuit,                 \[R=\frac{{{R}_{U}}\times {{R}_{L}}}{{{R}_{U}}\times {{R}_{L}}}=\frac{2R\times 2R}{2R+2R}=\frac{4{{R}^{2}}}{4R}=R\]