Given below are two statements : Statement I : A uniform wire of...

Statement $1 -$ $R = 80Ω$

When it is cut into $4$ equal parts, the resistance of each part will be,

${R}_{1} = {R}_{2} = {R}_{3} = {R}_{4} = 20Ω$

When these resistances are connected in parallel,

${R}_{eq} = \dfrac{20}{4} = 5Ω$

Hence, the statement I is correct.

Statement 2 -

When the resistances are connected in parallel, the potential difference between them is same. Therefore, the power consumed can be written as,

$P = \dfrac{{V}^{2}}{R}$

$⇒ \dfrac{{P}_{1}}{{P}_{2}} = \left(\dfrac{{R}_{2}}{{R}_{1}}\right) = \dfrac{2}{3}$

Hence, statement II is incorrect.