Solution
Related Formula
Wheatstone bridge balance: (P)/(Q) = (R)/(S) I = EReqCore Logic
The wire has a total resistance of 4Ω and is bent into a square ABCD. Thus, each side of the square has a resistance of 1Ω.
The battery is connected across nodes A and C. A 2Ω resistor is connected across nodes B and D.
We can unfold this circuit diagram: Branches AB and BC form two series resistors on top (totaling 1Ω + 1Ω = 2Ω, but tapped at B). Branches AD and DC form two series resistors on bottom. The ratio of the arms is:
RABRBC = (1)/(1) = 1 and RADRDC = (1)/(1) = 1Step 1: Simplify Equivalent Resistance
Because the ratios are equal, it forms a balanced Wheatstone bridge.
The effective resistance across AC: Top branch: Rₜₒₚ = 1Ω + 1Ω = 2Ω Bottom branch: Rbottom = 1Ω + 1Ω = 2Ω
Req = (2 × 2)/(2 + 2) = 1 ΩStep 2: Calculate Current
Using Ohm's Law:
I = EReq = 2 ~V1 Ω = 2 ~APattern Recognition
Any symmetric square loop driven diagonally with a cross resistor constitutes a balanced Wheatstone bridge. Ignore the diagonal resistor completely.
Chapter Mix
Class 12 Physics: Current Electricity