A 12 cm long uniform wire is bent into a triangle ABC with sides 3 cm, 4 cm and 5 cm. Resistances between terminals AB, BC and CA are measured separately. Their ratio is: [Diagram: Image]
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A 12 cm long uniform wire is bent into a triangle ABC with sides 3 cm, 4 cm and 5 cm. Resistances between terminals AB, BC and CA are measured separately. Their ratio is: [Diagram: Image]

G1 Physics · Accepted Answer

Step 1: Resistance proportional to length. Take AB=3r, BC=4r, CA=5r. Step 2: For AB, direct 3r in parallel with other path (4+5)r=9r; Rₐᵦ=(3×9)/(3+9)r=9r/4. Step 3: For BC, 4r||(3+5)r = (4×8/12)r=8r/3. Step 4: For CA, 5r||(3+4)r=(5×7/12)r=35r/12. Step 5: Multiply ratios by 12 ⇒ 27:32:35.