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As shown in the figure, balanced condition of Wheatstone Bridge is n= ________.

Asked in GUJCET 2025 · Wheatstone bridge

• (1) 3/2
• (2) 2/5
• (3) 1/2
• (4) 5/2

Step-by-step solution

Why the other options are wrong

• (1) 3/2 is (15)/(10), the ratio of the two upper arms, read off as the answer. Balance makes that ratio equal to n+1, not to n, so n=3/2-1=1/2.
• (2) No single slip produces 2/5; it is simply the reciprocal of 5/2. Sanity check: at n=2/5 the parallel pair is r with (5r)/2, which is (5r)/7, so the lower ratio is 7/5 and not the 3/2 that balance demands.
• (4) Combines the parallel pair as product over difference instead of product over sum. That makes the arm r/(n-1), balance then reads (15)/(10)=n-1, and n comes out as 5/2. Two resistors in parallel add their conductances, so the arm is r/(n+1).

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