Match List-I with List-II for the equivalent capacitance of...

(A) For three identical capacitors in series, the equivalent capacitance $C_s$ is given by:
$\dfrac{1}{C_s} = \dfrac{1}{C} + \dfrac{1}{C} + \dfrac{1}{C} = \dfrac{3}{C} \Rightarrow C_s = \dfrac{C}{3}$

(B) For three identical capacitors in parallel, the equivalent capacitance $C_p$ is:
$C_p = C + C + C = 3C$

(C) For two capacitors in series, their equivalent is $\dfrac{C}{2}$. When connected in parallel with the third capacitor, the total equivalent capacitance is:
$C_{eq} = \dfrac{C}{2} + C = \dfrac{3C}{2}$

(D) For two capacitors in parallel, their equivalent is $2C$. When connected in series with the third capacitor, the total equivalent capacitance is:
$C_{eq} = \dfrac{2C \times C}{2C + C} = \dfrac{2C^2}{3C} = \dfrac{2C}{3}$

Therefore, the correct match is (A) $\rightarrow$ (II), (B) $\rightarrow$ (I), (C) $\rightarrow$ (IV), (D) $\rightarrow$ (III).

Answer: (A) $\rightarrow$ (II), (B) $\rightarrow$ (I), (C) $\rightarrow$ (IV), (D) $\rightarrow$ (III)