Two parallel plate capacitors X and Y are connected in series to a 6 V battery. They have the same plate area and same plate separation but capacitor…

Calculating the capacitance of $\displaystyle \mathrm{X} \& \mathrm{Y}$.

Calculating the potential difference across plates of X & Y

$\displaystyle \mathrm{C}_{\mathrm{X}}=\mathrm{C}, \mathrm{C}_{\mathrm{Y}}=\mathrm{KC}=4 \mathrm{C}$

\[\begin{aligned} & \frac{1}{\mathrm{C}_{e q}}=\frac{1}{\mathrm{C}_{\mathrm{X}}}+\frac{1}{\mathrm{C}_{\mathrm{Y}}} \\ & \mathrm{C}_{e q}=\frac{\mathrm{C}_{\mathrm{X}} \mathrm{C}_{\mathrm{Y}}}{\mathrm{C}_{\mathrm{X}}+\mathrm{C}_{\mathrm{Y}}} \\ & 4=\frac{\mathrm{C} \cdot 4 \mathrm{C}}{\mathrm{C}+4 \mathrm{C}} \end{aligned} \]

$\displaystyle \mathrm{C}=5 \mu \mathrm{~F}$

\[\begin{aligned} & \mathrm{C}_{\mathrm{X}}=5 \mu \mathrm{~F} \\ & \mathrm{C}_{\mathrm{Y}}=20 \mu \mathrm{~F} \end{aligned} \]

Total charge $\displaystyle \mathrm{Q}=\mathrm{C}_{\mathrm{eq}} \mathrm{V}$

\[\begin{aligned} & =4 \times 10^{-6} \times 6 \\ & =24 \times 10^{-6} \mathrm{C} \end{aligned} \]