A wire of total resistance R is bent into a triangular pyramid as shown in the original figure, with all six segments of equal length. The equivalent resistance between vertices A and B is R/n. Find n.

Question

G1 Physics · Accepted Answer

The tetrahedral frame has six equal wire segments, so resistance of each segment is r = R/6. By symmetry, the two vertices other than A and B are at the same potential. Hence the branch joining those two equipotential vertices carries no current and can be ignored. Between A and B there are then three parallel paths: • direct path: r, • upper path: 2r, • inner path: 2r. Therefore, 1/ R A B R_AB R A ​ B = 1/r + 1/(2r) + 1/(2r) = 2/r. Thus, R A B R_AB R A ​ B = r/2 = (R/6)/2 = R/12. Hence n = 12.…