Chapter 27 - Capacitors and Batteries

• What is a capacitor?

  A device that consists of two conductors known as plates separated by an insulator or vacuum.
• What happens to the charges on the plates of a charged capacitor?

  One plate becomes positive and the other has an equal magnitude of negative charge.
• What is the purpose of a capacitor?

  • To store electric potential energy.
  • To maintain a charge difference between plates.
  • To release energy when needed.
• What are the types of insulators that can be used in capacitors?

  Air, plastic, or a vacuum.
• How do the plates of a capacitor relate to its function?

  The plates store electric charge, which creates an electric field and stores energy.
• What happens to the potential difference between the plates as the amount of charge increases?

  The potential difference increases.
• How is the potential difference ΔV related to the charge Q on each plate?

  ΔV is directly proportional to Q.
• What is the equation that relates charge Q, capacitance C, and potential difference ΔV?

  Q = CΔV
• What is the SI unit for capacitance?

  The farad (F).
• How can farads be expressed in terms of coulombs and volts?

  1 F = 1 C/V.
• What factors does capacitance depend on?

  Capacitance depends on geometric factors and the type of insulator.
• If two capacitors have the same potential difference, how does their capacitance affect the charge stored?

  The capacitor with greater capacitance stores more charge.
• What does a capacitor with greater capacitance do in terms of electric potential energy?

  It stores more electric potential energy.
• What is the relationship between capacitance and electric potential energy stored in a capacitor?

  A capacitor with greater capacitance stores more electric potential energy.
• Potential energy stored in a capacitor is given by $U_E =$$\frac{1}{2}\frac{Q^2}{C}$ and $U_E =$$\frac{1}{2}C \Delta V^2$
• An ideal battery is a device that maintains its terminal potential through chemical reactions.
• Equivalent capacitance of capacitors in series: \frac{1}{C_{eq}} = \sum_{i=1}^{N} \frac{1}{C_i}
• Equivalent capacitance of capacitors in parallel \frac{1}{C_{eq}} = \sum_{i=1}^{N} C_i
• Capacitance in the presence of a dielectric: C = \kappa C_{vac} = \kappa \frac{epsilon_0 A}{d}
• Energy density for a capacitor: u_E = \frac{1}{2}\kappa \epsilon_0 E^2