Question

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. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (C)

$C_1=\frac{{\epsilon }_{0}A}{3}$ before
$C_1=\frac{k{\epsilon }_{0}A}{3}+\frac{{\epsilon }_{0}A}{2\cdot 4}$ after
$\frac{{\epsilon }_{0}A}{3}=\frac{k\frac{{\epsilon }_{0}A}{3},\frac{{\epsilon }_{0}A}{2.4}}{k\frac{{\epsilon }_{0}A}{3}+\frac{6_{0}A}{2.4}}$
$3k=2.4k+3$
$0.6k=3$
$\Rightarrow k=\frac{3}{0.6}$
$k=\frac{30}{6}=5$