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JEE MAINS 2024
25.01.23 S1
Question
A parallel plate capacitor has plate area 40 cm2 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 :
Select the correct option:
A
$24 \varepsilon_0 \mathrm{~F}$
B
$\frac{3}{10} \varepsilon_0 F$
C
$\frac{10}{3} \varepsilon_0 \mathrm{~F}$ (4)
D
$10 \varepsilon 0 \mathrm{~F}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$\begin{aligned} \frac{1}{C_{e q}} & =\frac{1}{C_1}+\frac{1}{C_2} \\ & =\frac{1}{K \epsilon_0 A}+\frac{1}{\epsilon_0 A} \\ & =\frac{1}{K \epsilon_0 A}+\frac{d-t}{\epsilon_0 A} \\ & =\frac{1 \times 10^{-3}}{5 \epsilon_0 \times 40 \times 10^{-4}}+\frac{1 \times 10^{-3}}{\epsilon_0 40 \times 10^{-4}} \\ \frac{1}{C_{e q}} & =\frac{1}{20 \epsilon_0}+\frac{1}{4 \epsilon_0} \\ C_{e q} & =\frac{20 \times 4 \epsilon_0}{24}=\frac{10 \epsilon_0}{3} \mathrm{~F}\end{aligned}$
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