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  4. A parallel plate capacitor has plate area 40 cm 2 and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5 . The capacitance of the system is :

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Q. A parallel plate capacitor has plate area $40\, cm ^2$ and plates separation $2\, mm$. The space between the plates is filled with a dielectric medium of a thickness $1 \,mm$ and dielectric constant $5$ . The capacitance of the system is :

JEE MainJEE Main 2023Electrostatic Potential and Capacitance

Solution:

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This can be seen as two capacitors in series combination so
$ \frac{1}{ C _{ eq }}=\frac{1}{ C _1}+\frac{1}{ C _2} $
$=\frac{1}{\frac{ K \in_0 A }{ t }}+\frac{1}{\frac{\in_0 A }{ d - t }}$
$ =\frac{ t }{ K \in_0 A }+\frac{ d - t }{\epsilon_0 A } $
$ =\frac{1 \times 10^{-3}}{5 \epsilon_0 \times 40 \times 10^{-4}}+\frac{1 \times 10^{-3}}{\epsilon_0 40 \times 10^{-4}} $
$ \frac{1}{ C _{ eq }}=\frac{1}{20 \epsilon_0}+\frac{1}{4 \epsilon_0} $
$ C _{ eq }=\frac{20 \times 4 \epsilon_0}{24}=\frac{10 \epsilon_0}{3} F $