Question

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in the circuit shown five resistances are connected. The equivalent resistance between the two points X and Y will be ?

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Step-by-step explanation ✅

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Answer 1

$\dashrightarrow \frac{1}{ R_1} = \frac{1}{10} + \frac{1}{10} \\ \dashrightarrow \frac{1}{ R_1} = \frac{2}{10} \: \: \: \: \: \: \: \: \: \: \\ \dashrightarrow R_1 = 5 \: \: \: \: \: \: \: \: \: \: \: \: \:$

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$\dashrightarrow \frac{1}{R_2} = \frac{1}{10} + \frac{1}{10} \\ \dashrightarrow \frac{1}{R_2} = \frac{2}{10} \: \: \: \: \: \: \: \: \: \: \\ \dashrightarrow \: R_2 = 5 \: \: \: \: \: \: \: \: \: \: \: \:$

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Now,

$\dashrightarrow \frac{1}{Re} = \frac{1}{5} + \frac{1}{5} + \frac{1}{20} \\ \dashrightarrow \frac{1}{Re} = \frac{9}{20} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \dashrightarrow Re = \frac{20}{9}ᘯ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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Answer 2

We found out that powers of 2 (2, 4, 8, 16...) can never be made by adding together consecutive numbers together.