Find the equivalent resistance between
A
and
B
.
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A triumph of mental topology and physical intuition.
May I ask you how did you obtain the 2D circuit from the 3D one? Thanks in advance.
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You can trace it out. Say, we start from point A, it is connected to four resistors. Just lay them flat. Then every pair of these four resistors are connect with a resistor. Just draw them. It is just a mirror image for B.
Hey! Hi five for a symmetric solution! Did the same way but without 2D diagram! R = 2 r 1 × 4 1 = 2 r = 2 Ω
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Same way :-)
same way :)
Thanks !! But this should not be stated in a solution. (This is one of my very first problems and I'll update the diagram soon.)
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Ya! Sorry for posting it here.... This is an old problem but i've seen it thése days only! I love solving problems whether old or new...
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We note that the circuit can be simplified as the left circuit in the figure below.
Due to symmetry, we note that the potentials of C , D , E and F with respect to A and B are the same. Therefore, there is no current flowing through the eight resistors between the four points. The eight resistors are equivalent to open circuits, therefore the right circuit in the figure is the final equivalent circuit. Then the equivalent resistance is:
R A B = ( 4 + 4 ) ∣ ∣ ( 4 + 4 ) ∣ ∣ ( 4 + 4 ) ∣ ∣ ( 4 + 4 ) = 8 ∣ ∣ 8 ∣ ∣ 8 ∣ ∣ 8 = 8 1 + 8 1 + 8 1 + 8 1 1 = 2 1 1 = 2