The space between the plates of a parallel-pl | vedclass

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Question

$C _1=\frac{5 \in_0 A / 2}{d / 2}=\frac{5 \in_0 A}{ d }=5 C$
$C _2=\frac{2 \in_0 A / 2}{d / 2}=\frac{2 \in_0 A}{ d }=2 C$
$C _1 \& C _2$

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$C _1=\frac{5 \in_0 A / 2}{d / 2}=\frac{5 \in_0 A}{ d }=5 C$
$C _2=\frac{2 \in_0 A / 2}{d / 2}=\frac{2 \in_0 A}{ d }=2 C$
$C _1 \& C _2$ in series.
$C^{\prime}=\frac{C_1 C_2}{C_1+C_2}=\frac{(5 C)(2 C)}{7 C}=\frac{10}{7} C$
$C _3=\frac{3 \in_0 A / 2}{d / 2}=3 C$
$C _4=\frac{2 \epsilon_0 A / 2}{d / 2}=2 C$
$C _4 \& C _3$ in series; $C ^{\prime \prime}=\frac{(2 C )(3 C )}{5 C }=\frac{6}{5} C$
$C ^{\prime} \& C ^{\prime \prime}$ in parallel;
So, $C _{ eq }= C \left(\frac{6}{5}+\frac{10}{7}\right)= C \left(\frac{42+50}{35}\right)=\left(\frac{92}{35}\right) C$
$\frac{92}{35} C =\frac{ nC }{3}$
$n =\frac{92 \times 3}{35}=7.9 \Rightarrow n \simeq 8$

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