Capacitance Final Study Guide:

  • Formulas

    • U = ½ CV² = Q²/2C

    • C = Kε₀A/d

    • charge of proton 1.6 × 10^-19

    • mass of proton 1.67 × 10 ^-27

    • mass of electron 9.1 × 10^-31

Capacitors

✔ Summary Table

Capacitor Arrangement

Charge

Voltage

Series

Same on each capacitor

Splits (different values)

Parallel

Splits (different values)

Same on each capacitor

🔥 Intuition (this helps for tests)

  • Series = same current path → same charge.

  • Parallel = same connection to battery → same voltage.

Capacitance is defined by geometry and material, NOT by charge or voltage.

  • Because Q and V automatically adjust themselves depending on the capacitor’s physical structure.
    The ratio Q/V stays fixed for a given capacitor.

Isolated capacitor → CHARGE REMAINS CONSTANT, E field remains constant

Dielectrics

  • Dielectrics increase capacitance

Energy

  • KE = qV

Batteries

  • Battery stays connected

    • VOLTAGE STAYS CONSTANT

    • Charge changes based on the relationship V = Q/C

    • Since V is fixed → E = V/d

  • Battery is removed → capacitor is isolated

    • Q is constant

    • V adjusts on the relationship V = Q/C

    • E is constant

Practice Problems