JEE MAIN - Physics (2021 - 16th March Evening Shift - No. 19)
In a parallel plate capacitor set up, the plate area of capacitor is 2 m2 and the plates are separated by 1 m. If the space between the plates are filled with a dielectric material of thickness 0.5 m and area 2 m2 (see fig.) the capacitance of the set-up will be __________$$\varepsilon $$o. (Dielectric constant of the material = 3.2) (Round off to the Nearest Integer)
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Answer
3
Explanation
$${C_1} = {{K{\varepsilon _0}A} \over {d/2}};{C_2} = {{{\varepsilon _0}A} \over {d/2}}$$
$${1 \over C} = {1 \over {{C_1}}} + {1 \over {{C_2}}} = {d \over {2K{\varepsilon _0}A}} + {d \over {2{\varepsilon _0}A}}$$
$${1 \over C} = {d \over {2{\varepsilon _0}A}}\left( {{{K + 1} \over K}} \right)$$
$$C = {{2{\varepsilon _0}AK} \over {d(K + 1)}} = {{2 \times 2 \times 3.2} \over {1 \times 4.2}}{\varepsilon _0} = 3.04{\varepsilon _0}$$
$${1 \over C} = {1 \over {{C_1}}} + {1 \over {{C_2}}} = {d \over {2K{\varepsilon _0}A}} + {d \over {2{\varepsilon _0}A}}$$
$${1 \over C} = {d \over {2{\varepsilon _0}A}}\left( {{{K + 1} \over K}} \right)$$
$$C = {{2{\varepsilon _0}AK} \over {d(K + 1)}} = {{2 \times 2 \times 3.2} \over {1 \times 4.2}}{\varepsilon _0} = 3.04{\varepsilon _0}$$
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