Three unequal resistors in parallel are equivalent to a resistance 1 ohm . If two of them are in the ratio 1: 2 and if no resistance value is fractional, then the largest of the three resistances in ohms is

Step-by-step solution

Let the three resistances are R₁, R₂ and R₃ . R₁ R₂ = 1 2 R₁=k, R₂=2 k In parallel, 1 R = 1 R₁ + 1 R₂ + 1 R₃ 1 1 = 1 k + 1 2 k + 1 R₃ 1 R₃ =1- 1 k - 1 2 k = 2 k-2-1 2 k = 2 k-3 2 k R₃= 2 k 2 k-3 If k=1 , then R₃ is found to be negative, which is impossible. If k=2 , then R₁=2, R₂=4, R₃=4R₂=R₃ , not satisfying the condition of the question that all resistance are unequal. If k=3 , then R₁=3, R₂=6R₃=2 Largest resistance =6