question_answer

In the network shown, each resistance is equal to R. The equivalent resistance between adjacent corners A and D is

A) \[R\]     

B)                    \[\frac{2}{3}R\]

C) \[\frac{3}{7}R\]            

D)        \[\frac{8}{15}R\]

Correct Answer: D

Solution :

[d] The equivalent circuit is as shown in figure. The resistance of arm AOD (= R + R) is in parallel to the resistance R of arm AD. Their effective resistance \[{{R}_{1}}=\frac{2R\times R}{2R\times R}=\frac{2}{3}R\] The resistance of arms AB, BC and CD is \[{{R}_{2}}=R+\frac{2}{3}R+R=\frac{8}{3}R\] The resistance \[{{R}_{1}}\] and \[{{R}_{2}}\] are in parallel. The effective resistance between A and D is \[{{R}_{3}}=\frac{{{R}_{1}}\times {{R}_{2}}}{{{R}_{1}}+{{R}_{2}}}=\frac{\frac{2}{3}R\times \frac{8}{3}R}{\frac{2}{3}R+\frac{8}{3}R}=\frac{8}{15}R\]