12 wires each of resistance r ohm are connected in the form of a skeleton cube.Find the equivalent resistance of the cube ,when a cell is joined across any 1 of the 12 wires forming the cube.

Solution plzzz

To find the equivalent resistance of the cube when a cell is joined across any one of the 12 wires forming the cube, we can use a combination of series and parallel resistors.

First, let's understand the arrangement of the wires in the cube. A skeleton cube has 12 edges, and a wire is present along each edge. So, if we imagine the cube, each wire is connected to two other wires forming a branch.

If we consider any one of the wires, we can see that it is connected in parallel with two other wires. So, when the cell is joined across this wire, the equivalent resistance will be the parallel combination of the resistance of this wire and the resistance of the other two wires connected in parallel to it.

Let's represent the resistance of each wire as r. When combining resistors in parallel, we use the formula:

1/Req = 1/r1 + 1/r2 + 1/r3

Since the three resistors are of equal resistance, we can write the above equation as:

1/Req = 1/r + 1/r + 1/r

Simplifying,

1/Req = 3/r

To find the equivalent resistance of the cube, we need to consider all 12 wires. Each wire is connected in parallel with two other wires, so we can use the formula:

1/Req_cube = 1/Req + 1/Req + 1/Req + ... (12 times)

Substituting the value of 1/Req (which we found earlier) into this equation,

1/Req_cube = 12 * (3/r)

Simplifying,

1/Req_cube = 36/r

Taking the reciprocal of both sides, we get:

Req_cube = r/36

Therefore, the equivalent resistance of the cube, when a cell is joined across any one of the 12 wires forming the cube, is given by r/36 ohm.