The capacitance of a parallel plate capacitor with air as medium is $6 μ F$ . With the introduction of a dielectric medium, the capacitance becomes $30 μ F$ . The permittivity of the medium is :
$(\in_{0} = 8.85 \times 1 0^{- 12} C^{2} N^{- 1} m^{- 2})$

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Answer 1

Capacitance of air capacitor
$C_{0} = \frac{ε _{0} A}{d} = 6 μ F$ ......... (i)
When a dielectric of permittivity $ε_{r}$ and dielectric constant K is introduced between the plates, then
Capacitance, $C = \frac{K ε _{0} A}{d} = 30 μ F$ ..... (ii)
Dividing eq. (ii) by (i), we get
$\frac{C}{C _{0}} = \frac{\frac{K ϵ _{o} A}{d}}{\frac{ε _{0} A}{d}} = \frac{3 0}{6}$
$\Rightarrow K = 5$
$∴$ permittivity of the medium
$ε_{0} = ε_{0} K$
$= 8.85 \times 1 0^{- 12} \times 5 = 0.44 \times 1 0^{- 10}$

Answer 2

Capacitance of air capacitor

C_{0} = \frac{ε _{0} A}{d} = 6 μ F

......... (i)
When a dielectric of permittivity

ε_{r}

and dielectric constant K is introduced between the plates, then
Capacitance,

C = \frac{K ε _{0} A}{d} = 30 μ F

..... (ii)
Dividing eq. (ii) by (i), we get

\frac{C}{C _{0}} = \frac{\frac{K ϵ _{o} A}{d}}{\frac{ε _{0} A}{d}} = \frac{3 0}{6}

\Rightarrow K = 5

∴

permittivity of the medium

ε_{0} = ε_{0} K

= 8.85 \times 1 0^{- 12} \times 5 = 0.44 \times 1 0^{- 10}

The capacitance of a parallel plate capacitor with air as medium is $6 μ F$ . With the introduction of a dielectric medium, the capacitance becomes $30 μ F$ . The permittivity of the medium is :
$(\in_{0} = 8.85 \times 1 0^{- 12} C^{2} N^{- 1} m^{- 2})$

$1.77 \times 1 0^{- 12} C^{2} N^{- 1} m^{- 2}$

$0.44 \times 1 0^{- 10} C^{2} N^{- 1} m^{- 2}$

$5.00 C^{2} N^{- 1} m^{- 2}$

$0.44 \times 1 0^{- 13} C^{2} N^{- 1} m^{- 2}$

Solution

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Electrostatic Potential and Capacitance

Shortcuts & Tips

Mindmap

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Diagram set

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Memorization tricks

Common misconceptions

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The capacitance of a parallel plate capacitor with air as medium is $6 μ F$ . With the introduction of a dielectric medium, the capacitance becomes $30 μ F$ . The permittivity of the medium is :
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The capacitance of a parallel plate capacitor in air is $2 μ F$ . If a dielectric medium is placed between the plates then the potential difference reduces to $\frac{1}{6}$ of the original value. The dielectric constant of the medium is :

The capacitance of a parallel plate capacitor is $2.5 μ F$ . When it is half-filled with a dielectric shown in the figure Its capacitance becomes $5 μ F$ , the dielectric constant of the dielectric is :

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