Cube resistance
Electricity and Magnetism
Level
pending
In an electrice network of 12 identical wires of equal resistance R as shown in fig. the effective resistance between A and G is???????
5r/6
12r
6r/2
1r
6r
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1 solution
The skeleton cube composed of 12 wires each of resistance r is shown in fig. Let a current 6i enter at the corner A. The same current goes out from the corner G. Since the resistant of each wire is same, the current divides itself in 3 equal parts at A. Thus a current 2i flows in each of the arms AB, AE and AD. At B, E and D these current again divided them in 2 equal parts i and i. Finally a current of 2i flows in each of the arms HG, CG and FG. These current combine at G so that the current 6i flows out from this point. Let the potential difference between points A and G be V. Now consider any circuit (e.g. ABCG) between A and G. Clearly 2ir+ir+2ir=V 5ir=V 1st equation Suppose the equivalent resistance between A and G is R, Then 6i*R=V 2nd equation
From equation 1st and 2nd 6i R=5i r R=5r/6