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Current Electricity question

2007 · Q111
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Current Electricity question

2007 · Q111

NEETPhysicsCurrent ElectricityMCQ+4 / −1
Three resistances, P, Q, R each of 2Ω\OmegaΩ and an unknown resistance S from the four arms of a Wheatstone bridge circuit. When a resistance of 6 Ω\OmegaΩ is connected in parallel to S the bridge gets balanced. What is the value of S?
  1. A
    3 Ω\OmegaΩ
  2. B
    6 Ω\OmegaΩ
  3. C
    1 Ω\OmegaΩ
  4. D
    2 Ω\OmegaΩ.
View written solutionFree

Correct answer: A

A balanced wheatstone bridge simply requires

PQ=RS⇒22=2S{P \over Q} = {R \over S} \Rightarrow {2 \over 2} = {2 \over S}QP​=SR​⇒22​=S2​

Therefore, S should be 2Ω\Omega Ω.
A resistance of 6Ω\Omega Ω is connected in parallel.
In parallel combination,

1R=1R1+1R2{1 \over R} = {1 \over {{R_1}}} + {1 \over {{R_2}}}R1​=R1​1​+R2​1​

12=16+1S{1 \over 2} = {1 \over 6} + {1 \over S}21​=61​+S1​

⇒S=3Ω\Rightarrow S = 3\Omega⇒S=3Ω

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