When two resistances R₁ and R₂ are connected in series and introduced into the left gap of a metre bridge and a resistance of 10 Ω is introduced into the right gap, a null point is found at 60 cm from left side. When R₁ and R₂ are connected in parallel and introduced into the left gap, a resistance of 3 Ω is introduced into the right gap to get null point at 40 cm from left end. The product R₁R₂ is _____ Ω².
Physics · Circular Motion
JEE Mains 29 January 2023 Shift 2 Evening Shift

Question

When two resistances R₁ and R₂ are connected in series and introduced into the left gap of a metre bridge and a resistance of 10 Ω is introduced into the right gap, a null point is found at 60 cm from left side. When R₁ and R₂ are connected in parallel and introduced into the left gap, a resistance of 3 Ω is introduced into the right gap to get null point at 40 cm from left end. The product R₁R₂ is _____ Ω².

Physics · Circular Motion

JEE Mains 29 January 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

First condition: (R₁+R₂)/10 = 60/40 = 3/2, hence R₁+R₂ = 15. Second condition: [R₁R₂/(R₁+R₂)]/3 = 40/60 = 2/3. Thus R₁R₂/[15×3] = 2/3, giving R₁R₂ = 30 Ω².