Chapter 8: Capacitance

capacitor

device used to store electrical charge and energy

dielectric

insulating material between parallel plates of capacitor

parallel capacitors

multiple different paths around the circuit

• capacitors add normally (Cp = C1 + C2)

• total charge is a ratio of C —> (Q1 + Q2)

• v is always the same

series capacitors

only one possible path around circuit

• add 1/Cs = 1/C1 + 1/C2

• charge is same for all capacitors

energy in capacitors

capacitors store energy:

• U = ½ Q²/C or ½ CV²

equal to the work it takes to push the charges on

dielectric

excess charge at the edge of the block

• make total charge at the plate smaller

• electric field decreases —> k = Eo/E where k > 1

• capacitance increases —> C = kCo

  • more charge moves to the plates to overcome the part that is cancelled out (constant V = constant Ed)

disconnected capacitor

Q is constant (charge)

• capacitance increases, voltage decreases C = Q/V

  • C = kCo and V = Vo/k

• energy decreases

  • U = ½ CV² = Uo/k

• electric field is smaller

  • E = V/d = Eo/k

capacitor connected to same battery

V is constant

• capacitance increases

  • Q = CV, C = kCo

• more charge is stored

  • Q = CV = kQo

• energy increases

  • U = ½ CV² = kUo

• electric field is constant

  • E = V/d = Eo