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Q.

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, the largest of the three resistance in ohm is

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a

4

b

6

c

8

d

12

answer is B.

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Detailed Solution

$Let R_{1} = R, R_{2} = 2 R, R_{3} \frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} \Rightarrow \frac{1}{1} = \frac{1}{R} + \frac{1}{2 R} + \frac{1}{R_{3}} \frac{1}{R_{3}} = 1 - \frac{3}{2 R} \Rightarrow R_{3} = \frac{2 R}{2 R - 3} R = 1 Ω, R_{3} = - ve wrong R = 2 Ω, R_{3} = 4 Ω same as R_{2}, wrong R = 3 Ω R_{3} = 2 Ω; R_{1} = 3 Ω, R_{2} = 6 Ω, R_{3} = 2 Ω Max = 6 Ω$

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