To solve the problem step by step, we will analyze the circuit in two parts: first when switch K1 is closed and K2 is open, and then when K1 is opened and K2 is closed.
### Part 1: K1 Closed and K2 Open
1. **Understanding the Circuit Configuration**:
- Initially, K1 is closed, allowing current to flow through the circuit, while K2 is open, preventing any current from flowing through that branch.
- We have three capacitors: C1, C2, and C3.
2. **Identifying Charges on Capacitors**:
- Let the charge on capacitor C1 be Q1, on C2 be Q2, and on C3 be Q3.
- Since K2 is open, capacitor C3 will not have any charge, so we have:
\[
Q3 = 0
\]
3. **Capacitors in Series**:
- Capacitors C1 and C2 are in series. In a series configuration, the charge on each capacitor is the same:
\[
Q1 = Q2 = Q
\]
- Therefore, we can denote the charge on both C1 and C2 as Q.
4. **Calculating Equivalent Capacitance**:
- The equivalent capacitance (C_eq) for capacitors in series is given by:
\[
\frac{1}{C_{eq}} = \frac{1}{C1} + \frac{1}{C2}
\]
- If we assume C1 = C2 = 1 µF, then:
\[
C_{eq} = \frac{C1 \cdot C2}{C1 + C2} = \frac{1 \cdot 1}{1 + 1} = \frac{1}{2} \, \mu F = 0.5 \, \mu F
\]
5. **Finding the Total Charge**:
- If the voltage across the series combination is V (let’s assume V = 9V), the total charge Q can be calculated using:
\[
Q = C_{eq} \cdot V = 0.5 \, \mu F \cdot 9V = 4.5 \, \mu C
\]
- Therefore, we find:
\[
Q1 = Q2 = 4.5 \, \mu C \quad \text{and} \quad Q3 = 0
\]
### Part 2: K1 Opened and K2 Closed
1. **Switching the Configuration**:
- Now, K1 is opened, and K2 is closed. The charge on C1 will remain the same because it is isolated from the circuit:
\[
Q1' = Q1 = 4.5 \, \mu C
\]
2. **Redistributing Charge**:
- Capacitors C2 and C3 are now in parallel since K2 is closed. The charge on C2 (Q2) will redistribute between C2 and C3.
- Since both capacitors have the same capacitance (1 µF), the charge will split equally:
\[
Q2' = Q3' = \frac{Q2}{2} = \frac{4.5 \, \mu C}{2} = 2.25 \, \mu C
\]
3. **Final Charges**:
- The final charges on each capacitor are:
\[
Q1' = 4.5 \, \mu C, \quad Q2' = 2.25 \, \mu C, \quad Q3' = 2.25 \, \mu C
\]
### Summary of Charges
- Initially (K1 closed, K2 open):
- \( Q1 = 4.5 \, \mu C \)
- \( Q2 = 4.5 \, \mu C \)
- \( Q3 = 0 \)
- After switching (K1 open, K2 closed):
- \( Q1' = 4.5 \, \mu C \)
- \( Q2' = 2.25 \, \mu C \)
- \( Q3' = 2.25 \, \mu C \)
