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
Explanation
(c) The capacitance of air capacitor
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ C_{0} = \frac{A\varepsilon_{0}}{d} = 3\mu F$ …(i)
When a dielectric of permittivity $\varepsilon_{r}$ and dielectric constant $K$ is introduced between the plates of the capacitor, then its capacitance
$\ \ \ \ \ \ \ \ \ \ \ \ \ C\ = \frac{KA\varepsilon_{0}}{d} = 15\ \mu F$ …(ii)
Dividing Eq. (ii) by Eq. (i)
$\ \ \ \ \ \ \ \ \ \ \ \ \frac{C}{C_{0}} = \ \frac{\frac{KA\varepsilon_{0}}{d}}{\frac{A\varepsilon_{0}}{d}} = \frac{15}{3}$
$\therefore$ $K = 5$
Permittivity of the medium
$\ \ \ \ \ \ \varepsilon_{r} = \ \varepsilon_{0}K$
$\ \ \ \ \ \ \ \ \ \ \ = 8.854 \times 10^{- 12} \times 5$
$\ \ \ \ \ \ \ \ \ \ \ = 44.27 \times 10^{- 12}$
$\ \ \ \ \ \ \ \ \ \ \ = 0.44 \times 10^{- 10}C^{2}N^{- 1}m^{- 2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.