Capacitors

CAPACITORS AND CAPACITANCE

Learning Objectives

• Understand effects of simple capacitors on capacitance, charge, and potential difference with changes in:
  • Size
  • Potential difference
  • Charge
• Calculate equivalent capacitance in series and parallel configurations.

What is a Capacitor?

• A device used to store electrical charge.
• Capable of being charged and discharged quickly, maintaining a charge indefinitely.
• Unit Measure for Capacitance: Farad (F).
  • 1 Farad = 1 Coulomb/Volt

Capacitance Formula

• Formula: [ C = \frac{Q}{V} ]
  • Where:
  • C = Capacitance (F)
  • Q = Charge (C)
  • V = Voltage (V)

Sample Problem 1: Charge Calculation

• Problem: Determine charge stored on capacitor (4 x 10^-6 F) across 12V battery.
  • Formula:
    [ C = \frac{Q}{V} ]
  • Calculation:
    [ 4 \times 10^{-6} = \frac{Q}{12} ]
    [ Q = 48 \times 10^{-6} C ]

Application of Capacitors in Memory Chips

• Random Access Memory (RAM):
  • Stores binary information (1s and 0s) using capacitors.
  • Charged capacitor represents a "1", and uncharged represents a "0".
  • Memory cells contain millions of capacitors, often coupled with transistors.
  • Example: Typical capacitor may have capacitance of 3 x 10^-14 F.
  • If voltage for "1" = 0.5V, calculate electrons moved.
  • Using:
    [ C = \frac{Q}{V} ]
  • Calculation:
    [ 3 \times 10^{-14} = \frac{Q}{0.5} ]
    [ Q = 1.5 \times 10^{-14} C ]
  • Electrons:
    [ # electrons = \frac{1.5 \times 10^{-14}}{1.6 \times 10^{-19}} \approx 93750 ]

Equivalent Capacitance

Capacitors in Series

• Total capacitance formula:
  [ \frac{1}{CT} = \frac{1}{C1} + \frac{1}{C2} + \frac{1}{C3} + … ]
• Total capacitance decreases compared to individual capacitors.
• Same current flows through all capacitors:
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