What If? The two capacitors of Problem 16 are now connected...

What If? The two capacitors of Problem 16 are now connected in series and to a $9.00-\mathrm{V}$ battery. Find (a) the equivalent capacitance of the combination, (b) the potential difference across each capacitor, and (c) the charge on each capacitor.

Key Concepts

Series Combination of Capacitors

When capacitors are connected in series, they are arranged end-to-end so that the same charge moves through each capacitor. This means that, regardless of the different capacitances, the charge stored on each capacitor is the same. The total voltage provided by the battery is divided across the individual capacitors.

Equivalent Capacitance

The overall or equivalent capacitance of capacitors in series is determined by taking the reciprocal of the sum of the reciprocals of the individual capacitances. Mathematically, this is expressed as 1/C_eq = 1/C1 + 1/C2 + ... + 1/Cn, which results in a smaller equivalent capacitance than any individual capacitor in the series.

Charge-Voltage Relationship

The fundamental relationship for a capacitor is given by Q = CV, where Q represents the charge stored, C is the capacitance, and V is the voltage across the capacitor. In a series circuit, since each capacitor has the same charge, the voltage across each capacitor can be determined by dividing the charge by its capacitance.

Voltage Division in Series Circuits

In a series circuit, the total voltage from the battery is divided among the capacitors based on their individual capacitances. Specifically, a capacitor with lower capacitance will have a higher voltage drop compared to one with higher capacitance, since the voltage drop across each capacitor is inversely proportional to its capacitance.

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