A combination of parallel plate capacitors is maintained at a certain potential difference. When a 3  …

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



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

1. $6$
2. $4$
3. $3$
4. $5$

Solution

Assume initial separation as $3 \mathrm{mm}$

each capacitance $C_1=\frac{{\epsilon }_{0}A}{3}$ before

$C_1=\frac{\frac{k{\epsilon }_{0}A}{3}.\frac{{\epsilon }_{0}A}{2.4}}{\frac{k{\epsilon }_{0}A}{3}+\frac{{\epsilon }_{0}A}{2.4}}$

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

$3k=2.4k+3$

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

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

Asked in: JEE Main 2017 (09 Apr Online)

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