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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.
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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