Question 65 of 380

Given below are two statements :
Statement I : A uniform wire of resistance $80\Omega$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be $5\Omega$.
Statement II : Two resistance $2R$ and $3R$ are connected in parallel in an electric circuit. The value of thermal energy developed in $3R$ and $2R$ will be in the ratio $3:2$.
In the light of the above statements, choose the most appropriate answer from the options given below

ABoth statement I and statement II are correctBBoth statement I and statement II are incorrectCStatement I is correct but statement II is incorrectDStatement I is incorrect but statement II is correct.

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Answer: (C) Statement I is correct but statement II is incorrect

Statement $1-$ $R=80\Omega$
When it is cut into $4$ equal parts, the resistance of each part will be,
${R}_{1}={R}_{2}={R}_{3}={R}_{4}=20\Omega$
When these resistances are connected in parallel,
${R}_{eq}=\dfrac{20}{4}=5\Omega$
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,
$P=\dfrac{{V}^{2}}{R}$
$\Rightarrow \dfrac{{P}_{1}}{{P}_{2}}=\left(\dfrac{{R}_{2}}{{R}_{1}}\right)=\dfrac{2}{3}$
Hence, statement II is incorrect.