MCQ
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$33.3$
- ✓$200$
✓
Answer
Correct option: D.
$200$
d
${\rm{C}} = \frac{{{ \in _0}{\rm{A}}}}{{\rm{d}}};{{\rm{C}}_1} = \frac{{{ \in _0}{\rm{A}}}}{{2{\rm{d}}}} = \frac{{\rm{C}}}{2}$
${\rm{C}} = \frac{{{ \in _0}{\rm{A}}}}{{\rm{d}}};{{\rm{C}}_1} = \frac{{{ \in _0}{\rm{A}}}}{{2{\rm{d}}}} = \frac{{\rm{C}}}{2}$
${C_2} = \frac{{5{ \in _0}A}}{{2d}} = \frac{5}{2}C$
$C_{e q}=C_{1}+C_{2}=3 C$
$\frac{\Delta \mathrm{C}}{\mathrm{C}} \%=\frac{2 \mathrm{C}}{\mathrm{C}} \times 100=200 \%$
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