GATE 2021 BM – Question 39
In the shown bridge, Vₛ=100 V, R₁=30 Ω,R₂=60 Ω,R₃=90 Ω,R₄=45 Ω,R₅=30 Ω. Find current through R₃ in the indicated left-to-right direction, in A to two decimals.
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Correct answer: (B) +0.21
Explanation
Set the lower supply node to zero and let midpoint voltages be a,b. KCL gives (a−100)/30+a/45+(a−b)/90=0 and (b−100)/60+b/30+(b−a)/90=0. These reduce to 6a−b=300 and −2a+11b=300, giving a=56.25,b=37.5 V. Thus I₃=(a−b)/90≈.20833 A, rounded +.21 A, B.