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A source of potential difference $\mathrm{V}$ is connected to the combination of two identical capacitors as shown in the figure. When key $\mathrm{ ' K '}$ is closed, the total energy stored across the combination is $\mathrm{ E_{1}.}$ Now key $\mathrm{ ' K '}$ is opened and dielectric of dielectric constant $\mathrm{ 5}$ is introduced between the plates of the capacitors. The total energy stored across the combination is now $\mathrm{ E_{2}. }$ The ratio $\mathrm{ E_{1} /E_{2}}$ will be :

Option: 1
$\frac{1}{10}$

Option: 2
$\frac{2}{5}$

Option: 3
$\frac{5}{13}$

Option: 4
$\frac{5}{26}$

Answers (1)

best_answer

When the key $\mathrm{' K '}$ is closed
The potential drop across C is $\mathrm{V}$

$\mathrm{ E_1=\frac{1}{2} C V^2+\frac{1}{2} C V^2=C V^2 }$

When the key $\mathrm{ 'K '}$ is open

$\mathrm{E_2=\frac{1}{2} C' v^2=\frac{1}{2}(5 c) v^2 }$

$\mathrm{\frac{E_1}{E_2}=\frac{c v^2}{\frac{1}{2} c^{\prime} v^2}=\frac{2}{5}}$

Hence (2) is correct option.

Posted by

Divya Prakash Singh

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