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(A) The capacitance formulas for different configurations are as follows:$1$. For a cylindrical capacitor of length $\ell$ and radii $r_1, r_2$,the ca

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$A-(iii), B-(iv), C-(ii), D-(i)$

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(A) The capacitance formulas for different configurations are as follows:$1$. For a cylindrical capacitor of length $\ell$ and radii $r_1, r_2$,the capacitance is $C = \frac{2\pi \epsilon_0 \ell}{\ln(r_2/r_1)}$. Thus,$A \rightarrow iii$.$2$. For a spherical capacitor with inner radius $r_1$ and outer radius $r_2$,the capacitance is $C = \frac{4\pi \epsilon_0 r_1 r_2}{r_2 - r_1}$. Thus,$B \rightarrow iv$.$3$. For a parallel plate capacitor with a dielectric of constant $K$,the capacitance is $C = \frac{K A \epsilon_0}{d}$. Thus,$C \rightarrow ii$.$4$. For an isolated spherical conductor of radius $R$,the capacitance is $C = 4\pi \epsilon_0 R$. Thus,$D \rightarrow i$.Therefore,the correct matching is $A-(iii), B-(iv), C-(ii), D-(i)$.

Capacitor Type	Capacitance Formula
$A$. Cylindrical capacitor	$i$. $4\pi \epsilon_0 R$
$B$. Spherical capacitor	$ii$. $\frac{K A \epsilon_0}{d}$
$C$. Parallel plate capacitor with dielectric	$iii$. $\frac{2\pi \epsilon_0 \ell}{\ln(r_2/r_1)}$
$D$. Isolated spherical conductor	$iv$. $\frac{4\pi \epsilon_0 r_1 r_2}{r_2 - r_1}$

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