Six resistors are arranged along the edges of a pyramid as shown below. The values of the resistances are shown in the figure.

How can I find the effective resistance between A and B?

1 vote

Six resistors are arranged along the edges of a pyramid as shown below. The values of the resistances are shown in the figure.

How can I find the effective resistance between A and B?

closed with the note:
No Effort.

You could try applying Kirchhoff's Rules.

Alternatively, redraw the diagram in 2D as a triangle (ABC) with central point (D), with resistors connecting each pair of points. The resistors around the central point D form a Y or 'star' shape. This can be turned into an equivalent 'delta' $\Delta$ shape using the $Y-\Delta$ or 'star-delta' transform (look it up). This leaves you with inner and outer triangles, each side being parallel resistors, which is easily reduced further and solved.

This question looks to me as a objective type question which is to be solved within 3-4 minutes.so star delta transform but would be too lengthy and time consuming.instead this question can be solved by using symmetry .points D and C are equipotential points so we can removed the branch CD which then becomes simple series and parallel combination of resistances.

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