A parallel plate air capacitor has a capacitance C . When it is half filled with a dielectric

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2. Electric Potential and Capacitance

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A parallel plate air capacitor has a capacitance $C$. When it is half filled with a dielectric of dielectric constant $5$, the percentage increase in the capacitance will be......$\%$

A

$400$

B

$66.6$

C

$33.3$

D

$200$

Solution

${\rm{C}} = \frac{{{ \in _0}{\rm{A}}}}{{\rm{d}}};{{\rm{C}}_1} = \frac{{{ \in _0}{\rm{A}}}}{{2{\rm{d}}}} = \frac{{\rm{C}}}{2}$

${C_2} = \frac{{5{ \in _0}A}}{{2d}} = \frac{5}{2}C$

$C_{e q}=C_{1}+C_{2}=3 C$

$\frac{\Delta \mathrm{C}}{\mathrm{C}} \%=\frac{2 \mathrm{C}}{\mathrm{C}} \times 100=200 \%$

Standard 12

Physics

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(AIIMS-1997)