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Asked in GUJCET 2024 · Wheatstone bridge
Given: from the figure AB=2 Ω, BC=4 Ω, AD=4 Ω, DC=8 Ω, a galvanometer of 10 Ω between B and D, and a cell of 10 V across A and C.
Idea: before combining anything, test the bridge for balance. (AB)/(BC)=2/4 and (AD)/(DC)=4/8, and both equal 1/2.
The bridge is balanced, so B and D sit at the same potential and no current crosses the 10 Ω galvanometer branch. It can be left out of the sum.
Two paths then join A to C in parallel: 2+4=6 Ω through B, and 4+8=12 Ω through D.
R=(6×12)/(6+12)=4 Ω, so I=(10)/4=2.5 A.
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