Topic: Current Electricity
Q. A wire frame in the form of a tetrahedron ABCD is connected to a d.c. source.

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Figure-1

The resistances of all the edges of the tetrahedron are equal. Which edge of the frame should be eliminated to obtain the maximum change in the current in the circuit?

The first observation to be made is that by symmetry, there is no current in CD. If the resistance of each edge is R, then the net resistance Rnet between A and B is

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Now, we have to remove an edge. Note that the edges AD, AC, BD, BC are equivalent in the sense that the effect will be the same for any of them being removed. Suppose that the edge AD is removed. The net resistance R1 between A and B now is:

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Now suppose that AB is removed. In this case, the net resistance R2 between A and B is:

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Note that no current flows in this case in the edge CD, by symmetry. The new current is

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Therefore, the change in current is more in the second case:

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