Question

Twelve wires of equal resistance r are connected to form a cube. the effective resistance between two diagonal ends a and e will be

Answer 1

Twelve resistors (a, b, c, d, e, f, g, h, i, j, k, l) are connected in such a way that it create a cube. The corners of the cube are named as A, B, C, D, E, F, G, H in Fig.1 that is shown below in the picture.

The sides of the cube are considered as 1ω resistance. If we sort those nodes of the cube we can draw an equivalent circuit which is hsown in Fig.2.

As we can see, a, b, c are the set of three resistors connected parallelly which are in series with d, e, f, i, g, h six parallel resistors. And alo, these are serially connected with j,k, l three parallel resistors. The extreme nodes of Fig.2 are named as A and E. We have to calculate the equivalent resistance across A and E.

The middle nodes of Fig.2 are named as X and Y.

Equivalent resistance is 1/R(AX)= 1/a+1/b+1/c

So, R(AX) = 1/3ω

Now, 1/R(XY) = 1/i+1/g+1/h+1/d+1/e+1/f

Or, R(XY) = 1/6ω

Also, 1/R(YE) = 1/j+1/l+1/k

Or, R(YE) = 1/3ω

Now, AX, XY, YE are connected in series. o, the equivalent resistance of node A and node E is R(AE) = R(AX)+R(XY)+R(YE).

Or, R(AE) = 1/3+1/6+1/3

Or, R(AE) = 5/6ω

Answer 2

Answer:

11

Explanation:

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