Question 248: Electrostatics & Capacitance

Question

C
o
is the capacitance of a parallel plate capacitor with air as a medium between the plates (as shown in Fig. 1). If half space between the plates is filled with a dielectric of relative permittivity $\varepsilon $
r
(as shown in Fig. 2), the new capacitance of the capacitor will be :
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l5wij2nr/87b8cdbb-24fb-4a15-ba7b-fc3e8667c1b8/3e630470-09c4-11ed-aacd-cd06ee4162a1/file-1l5wij2ns.png?format=png)

Accepted Answer

Capacitance of Fig. 1, ${C_0} = {{{\varepsilon _0}A} \over d}$
In Fig. 2, C
1
and C
2
are parallel with each other,
$	herefore$ Equivalent capacitance,
${C_{eq}} = {C_1} + {C_2}$
$ = {{{\varepsilon _0}A/2} \over d} + {{{\varepsilon _0}{\varepsilon _r}A/2} \over d}$
$ = {{{\varepsilon _0}A} \over {2d}} + {{{\varepsilon _0}{\varepsilon _r}A} \over {2d}}$
$ = {{A{\varepsilon _0}} \over {2d}}\left( {1 + {\varepsilon _r}} ight) = {{{C_0}} \over 2}\left( {1 + {\varepsilon _r}} ight)$
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l6dmlb0e/b9f26b4c-8992-4723-9800-9f382628dc94/740368f0-132d-11ed-941a-4dd6502f33e3/file-1l6dmlb0f.png?format=png)

Answer

${{{C_o}} \over 2}(1 + {\varepsilon _r})$

Answer

${C_o} + {\varepsilon _r}$

Answer

${{{C_o}{\varepsilon _r}} \over 2}$

Answer

${C_o}(1 + {\varepsilon _r})$

Electrostatics & Capacitance

C o is the capacitance of a parallel plate capacitor with air as a medium between the plates (as shown in Fig. 1). If half space between the plates is filled with a dielectric of relative permittivity \varepsilon r (as shown in Fig. 2), the new capacitance of the capacitor will be :

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