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QJEEM23Phc985: JEE Main 2023 Physics - Class 12 JEEM23Phc985 Solution: A parallel plate capacitor has plate area 40 cm and plates…

A parallel plate capacitor has plate area 40 cm 2^2 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 :

Multiple Choice Options

  • A 10ε0 F\mathrm{10\varepsilon_0~F}
  • B 24ε0 F\mathrm{24\varepsilon_0~F}
  • C 310ε0 F\mathrm{\frac{3}{10}\varepsilon_0~F}
  • D 103ε0 F\mathrm{\frac{10}{3}\varepsilon_0~F}

Step-by-Step Verified Solution

JEE Main 2023 (Online) 25th January Morning Shift Physics - Capacitor Question 38 English Explanation

This can be seen as two capacitors in series combination so

amp;1Ceq=1C1+1C2amp;=1K∈0 At+1∈0 A d−t\begin{aligned}& \frac{1}{\mathrm{C}_{\mathrm{eq}}}=\frac{1}{\mathrm{C}_1}+\frac{1}{\mathrm{C}_2} \\\\& =\frac{1}{\frac{\mathrm{K} \in_0 \mathrm{~A}}{\mathrm{t}}}+\frac{1}{\frac{\in_0 \mathrm{~A}}{\mathrm{~d}-\mathrm{t}}}\end{aligned}

amp;=tK∈0 A+d−tϵ0 Aamp;=1×10−35∈0×40×10−4+1×10−3∈040×10−4amp;1Ceq=120∈0+14∈0amp;Ceq=20×4∈024=10∈03 F\begin{aligned}& =\frac{\mathrm{t}}{\mathrm{K} \in_0 \mathrm{~A}}+\frac{\mathrm{d}-\mathrm{t}}{\epsilon_0 \mathrm{~A}} \\\\& =\frac{1 \times 10^{-3}}{5 \in_0 \times 40 \times 10^{-4}}+\frac{1 \times 10^{-3}}{\in_0 40 \times 10^{-4}} \\\\& \frac{1}{\mathrm{C}_{\mathrm{eq}}}=\frac{1}{20 \in_0}+\frac{1}{4 \in_0} \\\\& \mathrm{C}_{\mathrm{eq}}=\frac{20 \times 4 \in_0}{24}=\frac{10 \in_0}{3} \mathrm{~F}\end{aligned}

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