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JEE MAIN - Physics (2022 - 30th June Morning Shift - No. 10)

Co 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 :

JEE Main 2022 (Online) 30th June Morning Shift Physics - Capacitor Question 55 English

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

Explanation

JEE Main 2022 (Online) 30th June Morning Shift Physics - Capacitor Question 55 English Explanation

Capacitance of Fig. 1, $${C_0} = {{{\varepsilon _0}A} \over d}$$

In Fig. 2, C1 and C2 are parallel with each other,

$$\therefore$$ Equivalent capacitance,

$${C_{eq}} = {C_1} + {C_2}$$

$$ = {{{\varepsilon _0}A/2} \over d} + {{{\varepsilon _0}{\varepsilon _r}A/2} \over d}$$

$$ = {{{\varepsilon _0}A} \over {2d}} + {{{\varepsilon _0}{\varepsilon _r}A} \over {2d}}$$

$$ = {{A{\varepsilon _0}} \over {2d}}\left( {1 + {\varepsilon _r}} \right) = {{{C_0}} \over 2}\left( {1 + {\varepsilon _r}} \right)$$

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