question_answer

A regular hexagonal mesh using equal resistances each of \[2\Omega \]is made as shown below.

Then, equivalent resistance between terminals A and B is

A) \[\frac{8}{5}\Omega \]

B) \[\frac{5}{8}\Omega \]

C) \[\frac{3}{8}\Omega \]  

D) \[2\Omega \]  

Correct Answer: A

Solution :

We take current distribution as follows
Now, from loops 1 and 2, we have
\[2x-y-z=0\]	... (i)
\[2x-3z=0\]	... (ii)

So, \[\frac{x}{3}=\frac{z}{2}=k\](let) \[\Rightarrow \]\[x=3k,z=2k\]

Substituting these in Eq. (i), we get \[y=4k\]

Let R = Equivalent resistance between A

and B, then \[{{V}_{AB}}=R\,(2x+y).\]

\[\Rightarrow \]\[2ry=R\,(2x+y)\]or \[R=\frac{2ry}{2x+y}=\frac{4}{5}r\]

Here, \[r=2\Omega ,\]so \[R=\frac{8}{5}\Omega .\]