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| Electrical Cube (Posted on 2005-05-17) |
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A wire structure in the form of a cube has a resistance of one ohm in each edge. An electrical circuit is formed by connecting a one volt battery to a pair of diagonally opposed vertices of the cube. What is the current, in amperes, in the wire connecting the battery to the cube structure?
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Submitted by Bractals
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Rating: 2.5000 (2 votes)
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Solution:
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(Hide)
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Because of symmetry the current entering the cube splits into three equal parts at the first vertex, one of those three equal parts splits into two equal parts at the next vertex, and one of those two equal parts combines with an equal part at the next vertex, that combination combines with two other equal combinations at the next vertex before leaving the cube.
Therefore,
1 volt = (i/3)*(1 ohm) + (i/6)*(1 ohm) + (i/3)*(1 ohm)
or
i = 6/5 amperes.
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