Charge Distribution on Capacitors After Sequential Switching

To determine the charge on the upper plates of capacitors $C_1$ and $C_2$, we follow the sequential switching operations step-by-step:

Step 1: Switch $S_1$ is closed and then opened

• The capacitor $C_1$ is connected across the DC source of emf $2V_0$, whose positive terminal is connected to the top wire and negative terminal to the bottom wire.
• Capacitor $C_1$ gets fully charged to a potential difference of $2V_0$.
• The charge on the upper plate of $C_1$ becomes: $Q_1 = C(2V_0) = 2CV_0$
• When $S_1$ is opened, capacitor $C_1$ retains this charge of $2CV_0$ on its upper plate.

---

Step 2: Switch $S_2$ is closed and then opened

• Closing $S_2$ connects the uncharged capacitor $C_2$ in parallel with $C_1$.
• The total charge on the isolated top plates of $C_1$ and $C_2$ is conserved: $Q_{\text{total}} = Q_1 + 0 = 2CV_0$
• Since both capacitors have identical capacitance $C$, the common potential $V_c$ is: $V_c = \frac{Q_{\text{total}}}{C + C} = \frac{2CV_0}{2C} = V_0$
• The charge on each capacitor's upper plate is distributed equally: $q_1 = C V_c = CV_0$ $q_2 = C V_c = CV_0$
• When $S_2$ is opened, capacitor $C_1$ is completely isolated from the rest of the circuit. Therefore, its charge remains unchanged at: $q_{\text{upper}, C_1} = CV_0$

---

Step 3: Switch $S_3$ is closed

• In the circuit diagram, the battery of emf $V_0$ in the rightmost branch is connected with its negative terminal at the top (short bar) and positive terminal at the bottom (long bar).
• When $S_3$ is closed, the capacitor $C_2$ is connected directly across this battery.
• After sufficient time has elapsed, the potential of the upper plate of $C_2$ relative to its lower plate becomes $-V_0$.
• Consequently, the steady-state charge on the upper plate of $C_2$ is: $q_{\text{upper}, C_2} = C(-V_0) = -CV_0$

---

Conclusion:

• The charge on the upper plate of $C_1$ is $CV_0$. (Option B)
• The charge on the upper plate of $C_2$ is $-CV_0$. (Option D)

Therefore, the correct options are B and D.