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

Step-by-step solution

The situation can be depicted as shown in figure. As resistances S and 6 are in parallel their effective resistance is 6 S 6+S As the bridge is balanced, hence it is balanced Wheatstone's bridge. For balancing condition, aligned & & P Q & = R ( 6 S 6+S ) or & & 2 2 & = 2(6+S) 6 S or & & 3 S & =6+S or & & S & =3 aligned