Capacitance

1
Capacitance

• Capacitance is one way that an object can store
  electrical energy.
• Define capacitance as the ratio of the magnitude
  of the charge to the change in electrical
  potential

• Definition is misleading, since capacitance does
  not depend on charge at all

2
Parallel Plate Capacitors

• Let Q sA
• From Gausss Law, know E s/e0

• Capacitance is thus

3
Capacitors in serial

• Charge is the same on each plate
• Potential is different on each capacitor
• V1 for C1 and V2 for C2
• Total potential change is VTot V1 V2
• Capacitance is thus

4
Capacitors in parallel

• Potential is the same on each capacitor
• Charge is different on each capacitor
• Q1 for C1 and Q2 for C2
• Total charge is QTot Q1 Q2
• Capacitance is thus

5
Energy in capacitors

• Energy is stored in the electric field between
  the plates
• PE QDV
• If DV is linear, can replace it with the average,
  Vave

6
Dielectrics

• Material placed between the plates of a capacitor
• Reduces the potential V V0/k
• Increases the capacitance C kC0
• Reduces the electric field E E0/k
• k depends on atomic makeup of material
• Material creates internal field opposing original
  electric field