Capacitor in Series and Parallel; Parallel Capacitors; Series Capacitors

📘 Capacitors in Series and Parallel 

Just like resistors, capacitors can also be connected in series or parallel. But unlike resistors, the behavior of capacitors is exactly opposite:

• Resistors in series → total resistance increases

• Capacitors in series → total capacitance decreases

• Resistors in parallel → total resistance decreases

• Capacitors in parallel → total capacitance increases

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🔹 Capacitors in Series

• Net capacitance decreases.

• Formula:

$$\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots + \frac{1}{C_n}$$

For two capacitors:

$$C_{eq} = \frac{C_1 \times C_2}{C_1 + C_2}$$

📌 Example:
C1 = 100 nF, C2 = 10 nF

$$C_{eq} = \frac{100 \times 10}{100 + 10} = 9.09 \, nF$$

• Key points:

  • Voltage rating adds up (useful when higher working voltage is required).

  • Charge stored is the same across all capacitors.

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🔹 Capacitors in Parallel

• Net capacitance increases.

• Formula:

$$C_{eq} = C_1 + C_2 + \dots + C_n$$

📌 Example:
C1 = 100 nF, C2 = 10 nF

$$C_{eq} = 100 + 10 = 110 \, nF$$

• Key points:

  • Working voltage stays the same as the lowest-rated capacitor.

  • Charge distribution depends on capacitance values.

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🔹 SI Prefixes for Capacitors

• 1 µF (microfarad) = 1,000 nF = 1,000,000 pF

• 1 nF (nanofarad) = 1,000 pF

• 1 pF (picofarad) = smallest practical capacitor unit

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⚠️ Notes

1. Polarity (for electrolytic capacitors):

   • Series → connect + of one to – of the next.

   • Parallel → connect all + together, all – together.

2. Voltage rating:
   Always choose a capacitor with a higher voltage rating than the applied voltage.
   Example: For 24V supply, use 35V capacitor instead of 16V.

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✅ Comparison Summary

Feature	Series Capacitors	Parallel Capacitors
Total Capacitance	Decreases (smaller than the smallest)	Increases (sum of all)
Working Voltage	Increases (adds up)	Same as lowest capacitor
Charge Distribution	Same across all	Divided based on C value
Best Use Case	Higher voltage handling	Higher capacitance storage

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