Question 112 of 180

A combination of parallel plate capacitors is maintained at a certain potential difference.



When a $3mm$ thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by $2.4mm$. Find the dielectric constant of the slab.

A$6$B$4$C$3$D$5$

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Answer: (D) $5$

Assume initial separation as $3mm$

each capacitance ${C}_{1}=\dfrac{{\epsilon }_{0}A}{3}$ before

${C}_{1}=\dfrac{\dfrac{k{\epsilon }_{0}A}{3}.\dfrac{{\epsilon }_{0}A}{2.4}}{\dfrac{k{\epsilon }_{0}A}{3}+\dfrac{{\epsilon }_{0}A}{2.4}}$

to get same capacitance $\dfrac{{\epsilon }_{0}A}{3}=\dfrac{k\dfrac{{\epsilon }_{0}A}{3}.\dfrac{{\epsilon }_{0}A}{2.4}}{k\dfrac{{\epsilon }_{0}A}{3}+\dfrac{{\epsilon }_{0}A}{2.4}}$

$3k=2.4k+3$

$0.6k=3\Rightarrow k=\dfrac{3}{0.6}$

$k=\dfrac{30}{6}=5$.