Charge stored in capacitor C3 in a given network

To find the charge stored in capacitor $C_3$, we analyze the potential difference across its terminals using the circuit diagram provided.

1. Identification of Nodes and Connections:

   • Let the bottom wire connecting the bottom plates of capacitors $C_3, C_4, C_5$ and the negative terminal of the $2\text{ V}$ battery be at a reference potential of $V_{\text{bottom}} = 0\text{ V}$.
   • The rightmost branch contains an ideal battery of potential difference $2\text{ V}$. Thus, the top wire connecting the positive terminal of the $2\text{ V}$ battery to the top plates of capacitors $C_3, C_4,$ and $C_5$ is at a constant potential of: $V_{\text{top}} = 2\text{ V}$

2. Potential Difference across $C_3$:

   • Capacitor $C_3$ is connected directly between the top wire (at potential $V_{\text{top}} = 2\text{ V}$) and the bottom wire (at potential $V_{\text{bottom}} = 0\text{ V}$).
   • Therefore, the potential difference $V_3$ across capacitor $C_3$ is: $V_3 = V_{\text{top}} - V_{\text{bottom}} = 2\text{ V} - 0\text{ V} = 2\text{ V}$

3. Calculation of Charge on $C_3$:

   • The capacitance of $C_3$ is given as $C_3 = 4\text{ }\mu\text{F}$.
   • Using the relation $Q = C \cdot V$, the charge $Q_3$ stored in capacitor $C_3$ is: $Q_3 = C_3 \times V_3 = 4\text{ }\mu\text{F} \times 2\text{ V} = 8\text{ }\mu\text{C}$

Final Answer: The charge stored in $C_3$ is 8 $\mu\text{C}$.