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Question
You have three resistors of values 2 Ω, 3 Ω, and 5 Ω. How will you join them so that the total resistance is less than 1 Ω? Draw a diagram and find the total resistance.
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Solution
It is necessary to connect the resistors in parallel because we desire an effective resistance that is lower than the minimum value of the individual resistors.
∴ `1/"R" = 1/"R"_1 + 1/"R"_2 + 1/"R"_3`
`1/"R" = 1/2 + 1/3 +1/5`
= `(15 + 10 + 6)/30`
= `31/30`
∴ R = `30/31 < 1Ω`
R = 0.97 Ω
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