Question

Find the equivalent resistance between `A` and `B`.
(a)
(b)
( c)
(d) Each resistance is `R`

( e) .

Answer 1

(a) This diagram is symmetrical about `AB`, hence points on the perpendicular bisector of `AB` i.e, `X,Y` and `Z` are at same potential. The resistances between `X` and `Y, Y` and `Z`, are redundant, remove them and solve.

(b) Symmetry about `AB, X, Y` and `Z` are at some potential , remove resistance between `X` and `Y , Y, ` and `Z`

( c) Symmetry about `AB, X, Y, Z` and `W` are at same potential , remove resistance between `X` and `Y, Y` and `Z, Z` and `W`.

(d) Symmetry about `AB, X, Y, Z` and `W` are at same potential , remove resistance between `X` and `Y, Z` and `W`.

(e) Symmetry about perpendicular bisector of `AB` i.e., `XYZ`. hence the points `X, Y` and `Z` are at the same potential Remove resistance between `X` and `Y, Y` and `Z`.
.