# Equivalent resistance

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The figure shows a network of resistor each heaving value 12.
Find the equivalent resistance between points A and B.

I could not understand how to solve this problem .

But after seeing the answer I noticed that , they have assumed these points at asame potential and neglected the resistance between them .

I could not understand how they can be at same potential .

asked Dec 26, 2016
reshown Dec 26, 2016

The answer in your book is correct. The potential at each of the 4 circled nodes in your diagram (nodes D, E, F, G in the leftmost figure of my diagram below) is $\frac12(V_A+V_B)$. This is because the resistances along the paths AD=DB, ACE=EHB, ACF=FHB, and AG=GB.
Resistances CEH and CFH are in parallel and each is 24$\Omega$, so they can be replaced by one resistor CH of 12$\Omega$ (see rightmost figure).
You are left with 3 parallel combinations of resistors, ADB and AGB each of 24$\Omega$ and ACHB of 36$\Omega$. The equivalent resistance is 9$\Omega$.