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Three resistances P,Q,R each of 2Ω and an unknown resistances S form the four arms

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

Options

(a) 3Ω
(b) 6Ω
(c) 1Ω
(d) 2Ω

Correct Answer:

3Ω

Explanation:

A balanced wheatstone bridge simply requires P/ Q = R / s 2 / 2 = 2 / S
Therefore, S should be 2Ω. A resistance of 6Ω is connected in parallel. In parallel combination,
1/R = 1/R₁ + 1/R₂
1/2 = 1/6 + 1/S
S = 3Ω

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