The effective resistance between points $P$ and $Q$ of the electrical circuit shown in the figure is
IIT 2002, Medium
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In a circuit, any circuit element placed between points at the same potential can be removed, without affecting the rest of the circuit. Here, by symmetry, points $A$, $B$ and $C$ are at same potential, for any potential difference between $P$ and $Q$.
The circuit can therefore be reduced as shown below
Effective resistance ${R_{eq}} = \frac{{2Rr}}{{R + r}}$.
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