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  4. A combination of parallel plate capacitors is maintained at a certain potential difference. <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/a6fb26ecd1277e85f650f6426c18e325-.png /> When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4 mm. Find the dielectric constant of the slab.

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Q. A combination of parallel plate capacitors is maintained at a certain potential difference.
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When a $3\, mm$ thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by $2.4\, mm$. Find the dielectric constant of the slab.

JEE MainJEE Main 2017Electrostatic Potential and Capacitance

Solution:

$C_{1}=\frac{\varepsilon_{0} A}{3}$ before
$C_{1}=\frac{k \varepsilon_{0} A}{3}+\frac{\varepsilon_{0} A}{2 \cdot 4}$ after
$\frac{\varepsilon_{0} A}{3}=\frac{k \frac{\varepsilon_{0} A}{3}, \frac{\varepsilon_{0} A}{2.4}}{k \frac{\varepsilon_{0} A}{3}+\frac{6_{0} A}{2.4}}$
$3 \,k=2.4 \,k+3$
$0.6\, k=3 $
$\Rightarrow k=\frac{3}{0.6}$
$k=\frac{30}{6}=5$