A source of potential difference V is connected to the combination of two identical capacitors as shown in the figure. When key ‘K’ is closed, the total energy stored across the combination is E₁. Now key ‘K’ is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now E₂. The ratio E₁/E₂ will be:

<p>I &gt; When switch is closed</p><p>Ceq = 2C</p><p>Energy E1 =&nbsp;<math><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>×</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>e</mi><mi>q</mi></mrow></msub><mo>×</mo><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>×</mo><mn>2</mn><mi>C</mi><mo>×</mo><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></p><p>E1 = CV2</p><p>II &gt; When switch is opened</p><p><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>×</mo><mrow><mo> (</mo><mrow><mn>5</mn><mi>c</mi></mrow><mo>)</mo></mrow><mo>×</mo><msup><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mfrac><mrow><msup><mrow><mrow><mo> (</mo><mrow><mi>C</mi><mi>v</mi></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn><mo>×</mo><mn>5</mn><mi>C</mi></mrow></mfrac></mrow></math></p><p><math><mrow><mo>=</mo><mfrac><mrow><mn>1</mn><mn>3</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mi>C</mi><msup><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></p><p><math><mrow><mo>⇒</mo><mfrac><mrow><msub><mrow><mi>E</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>E</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>1</mn><mn>3</mn></mrow></mfrac></mrow></math></p>

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