A cube is formed with ten identical resistances $R$ (thick lines) and two shorting wires (dotted lines) along the arms $A C$ and $B D$ as shown in the figure below. Resistance between point $A$ and $B$ is ...........$\Omega$
KVPY 2012, Diffcult
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(a)
First we connect points of equal potentials and redraw equivalent circuit.
Above equivalent circuit is a combination of two balanced Wheat stones bridge.
Hence, simplified circuit is
In above circuit, resistance combination gives,
So, equivalent resistance between $A$ and $B$ is $R_{A B}=\frac{R}{2} \,\Omega .$
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