Kirchoffs Laws Resistor Cube There are 12 resistors one alo

Kirchoffs Laws - Resistor Cube

There are 12 resistors, one along each edge. A voltage source is connected across a body diagonal of the cube. Using Kirchoffs Laws, we should be able to setup a 6x6 resistance matrix that can be solved to determine the total resistance. I AM LOOKING FOR THE FORM OF THE 6X6 MATRIX AND HOW IT IS ARRIVED AT. You do not need to solve it. Thanks.

Solution

We can write six different linear equations from the six different paths possible from A to B and use those six eqautons to find the net resistance between A and B.

Initially from point A we can take 3 different paths and from those three different paths we can again take 2 different ones . Hence it makes the totat ways as 3 x 2 = 6 .

Hence by combining these equation the 6X6 resistance matrix will be found.

(Hope you now can try wrting the equation and making the matrix, comment below if you still have doubts , otherwise please give a thumbs up)