Question 164: Electrostats & Capacitance

Question

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 :

Accepted Answer

This can be seen as two capacitors in series combination so
$$
\begin{aligned}
& \frac{1}{\mathrm{C}_{\mathrm{eq}}}=\frac{1}{\mathrm{C}_1}+\frac{1}{\mathrm{C}_2} \\
& =\frac{1}{\frac{\mathrm{K} \in_0 \mathrm{~A}}{\mathrm{t}}}+\frac{1}{\frac{\in_0 \mathrm{~A}}{\mathrm{~d}-\mathrm{t}}}
\end{aligned}
$$
$$
\begin{aligned}
& =\frac{\mathrm{t}}{\mathrm{K} \in_0 \mathrm{~A}}+\frac{\mathrm{d}-\mathrm{t}}{\epsilon_0 \mathrm{~A}} \\
& =\frac{1 	imes 10^{-3}}{5 \in_0 	imes 40 	imes 10^{-4}}+\frac{1 	imes 10^{-3}}{\in_0 40 	imes 10^{-4}} \\
& \frac{1}{\mathrm{C}_{\mathrm{eq}}}=\frac{1}{20 \in_0}+\frac{1}{4 \in_0} \\
& \mathrm{C}_{\mathrm{eq}}=\frac{20 	imes 4 \in_0}{24}=\frac{10 \in_0}{3} \mathrm{~F}
\end{aligned}
$$

Answer

$$\mathrm{10\varepsilon_0~F}$$

Answer

$$\mathrm{24\varepsilon_0~F}$$

Answer

$$\mathrm{\frac{3}{10}\varepsilon_0~F}$$

Answer

$$\mathrm{\frac{10}{3}\varepsilon_0~F}$$

Electrostats & Capacitance

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 :

Choose the correct answer: