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Three resistances P, Q, R each of 2Ω and an unknown resistance 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?

1. 3Ω
2. 6Ω
3. 1Ω
4. 2Ω

Correct answer: 3Ω

Solution

In a balanced Wheatstone bridge, the ratio of resistances in one pair of opposite arms equals the ratio in the other pair. Here, P/Q = R/(S||6). Since P = Q = R = 2Ω, we have 2/2 = 2/(S||6). Simplifying, S||6 = 2Ω. Using the formula for parallel resistance, 1/(S||6) = 1/S + 1/6, solving gives S = 3Ω.

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