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In a Wheatstone bridge, the three arms contain resistances P, Q, and R, while the fourth arm consists of two resistors S1 and S2 connected in parallel. For the bridge to be in balance, which relation must hold?

1. P/Q = 2R/(S1 + S2)
2. P/Q = R(S1 + S2)/(S1S2)
3. P/Q = R(S1 + S2)/(2S1S2)
4. P/Q = R/(S1 + S2)

Correct answer: P/Q = R(S1 + S2)/(S1S2)

Solution

The correct option establishes the condition for balance in a Wheatstone bridge by relating the ratios of the resistances. When the bridge is balanced, the voltage across the parallel combination of S1 and S2 must equal the voltage across R, leading to the derived relationship that incorporates the product of the parallel resistances.

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