To increase the capacity of a parallel plate capacitor, one should introduce between the plate a she

Question

To increase the capacity of a parallel plate capacitor, one should introduce between the plate a sheet of\

Professor PC Thomas Classes · Answer

$$
\mathrm{C}_{\mathrm{a}}=\frac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}}
$$
$\mathrm{C}_{\mathrm{m}}=\frac{\varepsilon_{0} \varepsilon_{\mathrm{r}} \mathrm{A}}{\mathrm{d}}$
$C=\frac{\varepsilon_{0} A}{d-t+\frac{t}{\varepsilon_{r}}}$

With air as dielectric the capacity is $\mathrm{C}_{\mathrm{a}}=\frac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}}$.\ If the space between the plates is completely filled with a dielectric the capacity is $\mathrm{C}_{\mathrm{m}}=\frac{\varepsilon_{0} \varepsilon_{\mathrm{r}} \mathrm{A}}{\mathrm{d}}$. The capacity increases by a factor $\varepsilon_{\mathrm{r}}$. If it is partly filled with a dielectric, the capacity is $\mathrm{C}=\frac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}-\mathrm{t}+\frac{\mathrm{t}}{\varepsilon_{\mathrm{r}}}}$. The capacity increases, because $d-t+\frac{t}{\varepsilon_{r}}$ is less than $d$\ If a thin metal plate is introduced the capacity is $\mathrm{C}=\frac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}-\mathrm{t}}$. The capacity increases. If the metal plate fills the space between the plates, the capacitor becomes a single plate and capacity decreases. Thus to increase the capacity there are three methods. \ 1) Fill the space between the plates with a dielectric \ 2) Introduce a thin slab of dielectric in between the plates\ 3) Introduce a thin slab of a metal in between the plates