A uniform wire with a resistance of $27 Ω$ is divided into three equal pieces and then they are joined in parallel. Find the equivalent resistance of the parallel combination.

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Solution

The wire cut into 3 equal pieces. This means the resistance of each part $= \frac{27}{3} = 9 Ω$

Now, the three parts are connected in parallel.
$1 over R equals fraction numerator begin display style 1 end style over denominator R subscript 1 end fraction plus 1 over R subscript 2 plus 1 over R subscript 3 equals 1 over 9 plus 1 over 9 plus 1 over 9 equals 3 over 9 R equals 9 over 3 equals 3 space o h m$

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