Find the equivalent resistance of the network shown in figure between the points a and b when (a) the switch S is open and (b) the switch S is closed .

Explanation

(a) When the switch is open, `6(Omega) and 12(Omega) resistors on the upper line are in series giving an equivalent of`18(Omega)`.Similarly, the resistors on the lower line have equivalent resistance `18(Omega).` These two 18(Omega) resistances are connected in parallel between a and b so that the equivalent resistances is `9(Omega)`.
(b) when the switch is closed, the 6(Omega) and 12(Omega) resistors on the left are in parallel givinig an equivalent resistance of `4Omega`. Similarly the two resistors o the right half are equivalent to `4(Omega)`.These two are connected in series between a and b so that the equivalent resistance is `8(Omega).`