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$400$
- ✓$66.6$
- C$33.3$
- D$200$
✓
Answer
Correct option: B.
$66.6$
b
Initial capacitance $ = \frac{{{ \in _0}A}}{d}$
Initial capacitance $ = \frac{{{ \in _0}A}}{d}$
When it is half filled by a dielectric of dielectric constant $K$, then
$C_{1}=\frac{K \varepsilon_{0} A}{d / 2}=2 K \frac{\varepsilon_{0} A}{d}$
and $C_{2}=\frac{\varepsilon_{0} A}{d / 2}=\frac{2 \varepsilon_{0} A}{d}$
$\therefore \frac{1}{{{C^\prime }}} = \frac{1}{{{C_1}}} + \frac{1}{{{C_2}}} = \frac{d}{{2{\varepsilon _0}A}}\left( {\frac{1}{K} + 1} \right)$
$ = \frac{d}{{2{\varepsilon _0}A}}\left( {\frac{1}{5} + 1} \right) = \frac{6}{{10}}\frac{d}{{{\varepsilon _0}A}}$
$C = \frac{{5{\varepsilon _0}A}}{{3d}}$
Hence, $\%$ increase in capacitance
${ = \left( {\frac{{\frac{5}{3}\frac{{{\varepsilon _0}A}}{d} - \frac{{{\varepsilon _0}A}}{d}}}{{\frac{{{\varepsilon _0}A}}{d}}}} \right) \times 100}$
${ = \left( {\frac{5}{3} - 1} \right) \times 100 = \frac{2}{3} \times 100 = 66.6\% }$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
An $X$-ray tube has a short wavelength end at $0.45 \mathring A$. The voltage of tube is ........ $V$
→For the refraction of light through a prism
Which of the following graphs shows the variation of magnetic induction $B$ with distance $r$ from a long wire carrying current
→In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked $A. B, C. D$ and $E.$ The transitions $A , B$ and $C$ respectively represent
→A torch bulb rated as $4.5\, W, 1.5\, V$ is connected as shown in the figure. The $e.m.f.$ of the cell needed to make the bulb glow at full intensity is ............. $V$
→In a meter bridge the point D is a neutral point (Fig).
An optically active compound
Which of the following spectrum have all the frequencies from high to low frequency range
A parallel plate condenser has a capacitance 50μF in air and 110μF when immersed in an oil. The dielectric constant ‘k’ of the oil is
Two stars situated at distances of $1$ and $10 $ light years respectively from the earth appear to possess the same brightness. The ratio of their real brightness is
→