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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 diagram and find the total resistance.

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Solution

The three resistors should be connected in parallel to get a toal resistance less than 1 ohm

Let R' be the total resistance
then,
$fraction numerator 1 over denominator R apostrophe end fraction equals 1 half plus 1 third plus 1 fifth equals fraction numerator 15 plus 10 plus 6 over denominator 30 end fraction equals fraction numerator begin display style 31 end style over denominator 30 end fraction R apostrophe equals 30 over 31 equals 0.97 space o h m$

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