In a Wheatstone's bridge, three resistance 'Q', 'R' and 'S' are connected in three arms and first arm is formed by three resistances ' P₁ ', ' P₂ ' and ' P₃ ' in parallel. The condition for the bridge to be balanced is

Step-by-step solution

For a balanced Wheatstone bridge, the ratio of resistances in the adjacent arms must be equal. From the given circuit diagram, the resistances in the four arms are: Resistance of arm AB = P Resistance of arm BC = Q Resistance of arm AD = S Resistance of arm DC = R The condition for the bridge to be balanced is: P Q = S R The resistance P is formed by three resistors P₁ , P₂ , and P₃ connected in parallel. The equivalent resistance P is given by: 1 P = 1 P₁ + 1 P₂ + 1 P₃ 1 P = P₂ P₃ + P₁ P₃ + P₁ P₂ P₁ P₂ P₃ P = P₁ P