Three resistances P, Q, R each of 2  Ω and an unknown resistance S form the four arms of a Wheatstone's bridge circuit. When a resistance of 6  Ω is connected in parallel to s the bridge gets balanced. what is the value of S?

The bridge formed with given resistances is a balanced Wheatstone's bridgeThe situation can be depicted as shown in the figure.As resistances S and 6  Ω are in parallel, their effective resistance is 6S6+S Ω.For balancing condition, PQ = R6S6+Sor  22=26+S6S or    3S=6+S  ⇒  S=3  Ω