Capacitors Series
1. **State the problem:** Four capacitors $C_1, C_2, C_3,$ and $C_4$ are connected in series between terminals A and B.
2. **Given data:**
- Potential drops: $V_1 = 1$ V, $V_2 = 2$ V, $V_3 = 3$ V, $V_4 = 4$ V
- Charge on $C_3$: $Q_3 = 8 \mu C$
3. **Find:**
- Potential difference $V_{AB}$ between terminals A and B
- Charge stored by capacitor $C_1$, $Q_1$
4. **Key concept:** In series connection, the charge $Q$ on each capacitor is the same:
$$Q_1 = Q_2 = Q_3 = Q_4 = Q$$
5. **Calculate total potential difference:**
The total voltage across the series is the sum of individual voltages:
$$V_{AB} = V_1 + V_2 + V_3 + V_4 = 1 + 2 + 3 + 4 = 10 \text{ V}$$
6. **Charge on $C_1$:**
Since the capacitors are in series, the charge on each capacitor is equal:
$$Q_1 = Q_3 = 8 \mu C$$
**Final answers:**
- Potential difference between A and B:
$$V_{AB} = 10 \text{ V}$$
- Charge stored by capacitor $C_1$:
$$Q_1 = 8 \mu C$$