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  4. A cube is formed with ten identical resistances R (thick lines) and two shorting wires (dotted lines) along the arms AC and BD as shown in the figure below. <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/e3619599d596f357ad0e189028e8184d-.jpeg /> Resistance between point A and B is

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Q. A cube is formed with ten identical resistances $R$ (thick lines) and two shorting wires (dotted lines) along the arms $AC$ and $BD$ as shown in the figure below.
image
Resistance between point $A$ and $B$ is

KVPYKVPY 2012

Solution:

First we connect points of equal potentials and redraw equivalent circuit.
image
image
Above equivalent circuit is a combination of two balanced Wheat stones bridge. Hence, simplified circuit is
image
In above circuit, resistance combination gives,
image
So, equivalent resistance between $A$ and $B$ is $=\frac{R}{2}\Omega.$