Three unequal resistors in parallel are equivalent to a resistance 1 Ω . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, what will be the largest of the three resistance in ohm?

Step-by-step solution

Let the resistances be R 1 , R 2 and R 3 ∴ R 1 R 2 = 1 2 ⟹ R 1 = k , R 2 = 2 k In parallel 1 R = 1 R 1 + 1 R 2 + 1 R 3 1 1 = 1 k + 1 2 k + 1 R 3 1 R 3 = 1 - 1 k = 1 2 k = 2 k - 2 - 1 2 k = 2 k - 3 2 k R 3 = 2 k 2 k - 3 If k = 1, then R 3 is found to be negative, which is impossible. If k = 2, then R 1 = 2 , R 2 = 4 R 3 = 4 R 2 = R 3 , not satisfying the condition of the question that all resistance are unequal. I f k = 3 , t h e n R 1 = 3 , R 2 = 6 R 3 = 2 Ω ∴ Largest resistance = 6 Ω