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 :

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,
$${C_{eq}} = {C_1} + {C_2}$$
$$ = {{{\varepsilon _0}A/2} \over d} + {{{\varepsilon _0}{\varepsilon _r}A/2} \over d}$$
$$ = {{{\varepsilon _0}A} \over {2d}} + {{{\varepsilon _0}{\varepsilon _r}A} \over {2d}}$$
$$ = {{A{\varepsilon _0}} \over {2d}}\left( {1 + {\varepsilon _r}} ight) = {{{C_0}} \over 2}\left( {1 + {\varepsilon _r}} ight)$$

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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