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  4. A parallel plate air capacitor has a capacitance 18 μ F. If the distance between the plates is tripled and a dielectric medium is introduced, the capacitance becomes 72 μ F. The dielectric constant of the medium is

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Q. A parallel plate air capacitor has a capacitance $18\, \mu F$. If the distance between the plates is tripled and a dielectric medium is introduced, the capacitance becomes $72\, \mu F$. The dielectric constant of the medium is

Electrostatic Potential and Capacitance

Solution:

$C_{0}=\frac{\varepsilon_{0} A}{d}=18$
$C=\frac{K \varepsilon_{0} A}{3 d}=72$
On dividing Eq. (ii) by Eq. (i), we get
$\frac{K}{3}=\frac{72}{18}=4$
$\therefore$ Dielectric constant, $K=12$