Three resistances P, Q, R each of 2 Ω and an unknown resistance S form four arms of a Wheatstone bridge. When a resistance of 6 Ω is connected in parallel to S, bridge gets balanced. Value of S is:
Options

Question

Three resistances P, Q, R each of 2 Ω and an unknown resistance S form four arms of a Wheatstone bridge. When a resistance of 6 Ω is connected in parallel to S, bridge gets balanced. Value of S is:

G1 Physics · Accepted Answer

Step 1: Balanced bridge with P=Q=R=2 Ω requires effective fourth arm = 2 Ω. Step 2: S || 6 = 2 ⇒ (6S)/(S+6) = 2. Step 3: 6S = 2S+12 ⇒ S = 3 Ω.