Capacitors in series share:
AThe same charge Q
BThe same voltage
CDifferent charges
DEqual capacitance
Answer & Solution
Correct answer: A. The same charge Q
In a series circuit, capacitors are connected end-to-end such that there is only one path for the charge to flow.
1. **Charge Induction**: When a voltage source is applied across the series combination, electrons are pulled from the positive plate of the first capacitor and pushed onto the negative plate of the last capacitor.
2. **Internal Distribution**: This movement of charge induces an equal and opposite charge on the adjacent plates of each capacitor in the chain. Since the capacitors are 'in-line', the charge $Q$ that leaves one plate must arrive at the next.
3. **Mathematical Relationship**: For capacitors in series, the magnitude of charge on each plate is identical:
$$Q_{total} = Q_1 = Q_2 = Q_3 = \dots$$
In contrast, the total voltage is divided among the capacitors based on their capacitance ($V_{total} = V_1 + V_2 + \dots$), and the equivalent capacitance is given by:
$$\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots$$
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