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  4. The capacitance of a parallel plate capacitor with air as medium is 3 μ F . With the introduction of a dielectric medium between the plates, the capacitance becomes 15 μ F . The permittivity of the medium is

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Q. The capacitance of a parallel plate capacitor with air as medium is $ 3\,\mu F $ . With the introduction of a dielectric medium between the plates, the capacitance becomes $ 15\,\mu F $ . The permittivity of the medium is

BHUBHU 2010Electrostatic Potential and Capacitance

Solution:

Capacitance of a parallel plate capacitor with air is
$C=\frac{\varepsilon_{0} A}{d}$
Capacitance of a same parallel plate capacitor with the introductory of a dielectric medium
$C^{'}=\frac{k \varepsilon_{0} A}{d}$
where $k$ is the dielectric constant of a medium.
$\therefore \frac{C^{'}}{C}=k \rightarrow=\frac{15}{3}=5$
and $k=\frac{\varepsilon}{\varepsilon_{0}}$
or $\varepsilon=k \varepsilon_{0}=5 \times 8.854 \times 10^{-12}$
$=0.4427 \times 10^{-10}\, C^{2} \,N^{-1}\, m^{-2}$