### Capacitance Question 2

#### Question 2 - 25 January - Shift 1

A parallel plate capacitor has plate area $40 cm^{2}$ and plates separation $2 mm$. The space between the plates is filled with a dielectric medium of a thickness $1 mm$ and dielectric constant 5 . The capacitance of the system is :

(1) $24 \varepsilon_0 F$

(2) $\frac{3}{10} \varepsilon_0 F$

(3) $\frac{10}{3} \varepsilon_0 F$

(4) $10 \varepsilon_0 F$

## Show Answer

#### Answer: (3)

#### Solution:

#### Formula: Capacitor with Dielectric

This can be seen as two capacitors in series combination so

$\frac{1}{C _{eq}}=\frac{1}{C_1}+\frac{1}{C_2}$

$=\frac{1}{\frac{K \in_0 A}{t}}+\frac{1}{\frac{\epsilon_0 A}{d-t}}$

$=\frac{t}{K \epsilon_0 A}+\frac{d-t}{\epsilon_0 A}$

$=\frac{1 \times 10^{-3}}{5 \in_0 \times 40 \times 10^{-4}}+\frac{1 \times 10^{-3}}{\in_0 40 \times 10^{-4}}$

$\frac{1}{C _{eq}}=\frac{1}{20 \epsilon_0}+\frac{1}{4 \epsilon_0}$

$C _{\text{eq }}=\frac{20 \times 4 \in_0}{24}=\frac{10 \in_0}{3} F$