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

Given, uniform wire with a resistance of 27 ohm is divided into three equal pieces. Hence, resistance of each piece = 9 Ω.

Three such pieces are joined in parallel.

In parallel, if the equivalent resistance is R_P, then

$\dfrac{1}{R$P} = \dfrac{1}{R1} + \dfrac{1}{R2} + \dfrac{1}{R3} \\[0.5em] \dfrac{1}{RP} = \dfrac{1}{9} + \dfrac{1}{9} + \dfrac{1}{9} = \dfrac{3}{9} = \dfrac{1}{3} \\[0.5em] \Rightarrow RP = 3 Ω

Hence, equivalent resistance = 3 Ω