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Three unequal resistors in parallel are equivalent to resistance 1 Ω . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms is
  • a)
    4
  • b)
    6
  • c)
    8
  • d)
    12
Correct answer is option 'B'. Can you explain this answer?
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Three unequal resistors in parallel are equivalent to resistance 1 . ...
Given Information:
Three unequal resistors in parallel are equivalent to resistance 1. Two of the resistors are in the ratio 1:2.

Solution:

Let the resistances be R1, R2, and R3.

Given:
R1 + R2 + R3 = 1 ...(1)
R1 : R2 = 1 : 2

Let R1 = x, R2 = 2x
Therefore, R3 = 1 - (x + 2x) = 1 - 3x

Substitute the values of R1, R2, and R3 into equation (1):
x + 2x + 1 - 3x = 1
=> 3x - 3x = 0
=> x = 0
This implies R1 = 0, R2 = 0, and R3 = 1, which is not possible as resistances cannot be zero.

Let us now assume that R1 = 2x, R2 = x
Therefore, R3 = 1 - (2x + x) = 1 - 3x

Substitute the values of R1, R2, and R3 into equation (1):
2x + x + 1 - 3x = 1
=> 0 = 0
This means, the values of R1, R2, and R3 are correct.

Calculating the resistances:
R1 = 2x = 2 * 1 = 2 ohms
R2 = x = 1 ohm
R3 = 1 - 3x = 1 - 3 = 2 ohms

Hence, the largest resistance is 2 ohms, which corresponds to option (b).
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Three unequal resistors in parallel are equivalent to resistance 1 . If two of them are in the ratio 1 : 2 and if no resistance value is fractional, the largest of the three resistances in ohms isa)4b)6c)8d)12Correct answer is option 'B'. Can you explain this answer?
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