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 \[R=\frac{8}{5}\Omega .\] |
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