Combination of Capacitors in Series
2.14 COMBINATION OF CAPACITORS
We can combine several capacitors of capacitance \( C_1, C_2, ..., C_n \) to obtain a system with some effective capacitance \( C \). The effective capacitance depends on the way the individual capacitors are combined.
2.14.1 Capacitors in Series
When capacitors are combined in series, the left plate of the first capacitor and the right plate of the last capacitor are connected to the battery terminals. The magnitude of charge on all plates is the same (\( \pm Q \)).
For series combination:
\( \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n} \)
\( \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n} \)
2 μF
3 μF
6 V
Equivalent Capacitance: Calculating...
Key Observations:
- In series combination, all capacitors have the same charge \( Q \) on their plates.
- The total voltage is the sum of individual voltages across each capacitor.
- The equivalent capacitance is always less than the smallest individual capacitor in the series.
- Charge cannot flow between capacitors as they are separated by insulators, but the electric field causes charge redistribution.
