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 resistances 2R and 3R are connected in parallel in a 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 option given below

Correct Option - 3


Detailed Solution:

Statement – I

$80=\frac{\rho \mathcal{l}}{A}$

$So,R_{eq}=\frac{R\text{'}}{4}=\frac{20}{4}=5\Omega$

Statement – II

$\frac{P_1}{P_2}=\frac{V^2}{2R}\times \frac{3R}{V^2}=\frac{3}{2}$

 

<p><strong>Statement – I</strong></p><p><strong><math><mrow><mn>8</mn><mn>0</mn><mo>=</mo><mfrac><mrow><mi>ρ</mi><mi mathvariant="script">l</mi></mrow><mrow><mi>A</mi></mrow></mfrac></mrow></math></strong></p><p><strong><math><mrow><mi>S</mi><mi>o</mi><mo>, </mo><msub><mrow><mi>R</mi></mrow><mrow><mi>e</mi><mi>q</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi>R</mi><mo>'</mo></mrow><mrow><mn>4</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mn>0</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>=</mo><mn>5</mn><mi>Ω</mi></mrow></math></strong></p><p><strong>Statement – II</strong></p><p><strong><math><mrow><mfrac><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msup><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn><mi>R</mi></mrow></mfrac><mo>×</mo><mfrac><mrow><mn>3</mn><mi>R</mi></mrow><mrow><msup><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></strong></p><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1752473561phpmZqXwY.jpeg" alt="" width="324" height="303" loading="lazy"></picture></div></div><p>&nbsp;</p>

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