Question

A parallel plate capacitor is given a definite potential difference. Keeping the potential difference same, a slab of thickness 3 mm is placed between the plates. To do this, the distance between the plates is increased by 2.4 mm. Calculate the dielectric constant of the slab.

• A. 10
• B. 15
• C. 5
• D. 8

Answer 1

The correct option is C 5

$\frac{\epsilon A}{d}=\frac{{\epsilon }_{0}A}{d^{\prime }-t+\frac{r}{{\epsilon }_r}}$
or
$d=d^{\prime }-t+\frac{t}{{\epsilon }_r}$
$r-\frac{r}{{\epsilon }_r}=d^{\prime }-d=2.4mm$
$r\left(1-\frac{1}{{\epsilon }_r}\right)=2.4$
$1-\frac{1}{{\epsilon }_r}=\frac{2.4}{3}\Rightarrow {\epsilon }_r=\frac{30}{6}=5$