Post on 07-Mar-2018
Lecture 36
• Capacitance
• Combinations of capacitors (series and parallel)
• Energy stored in capacitor (electric field)
• start chapter 31 (Fundamentals of Circuits)
Capacitance
Combinations...
!Vc = 0 !Vwire = 0
V = Ed; E = Q!0A ;
C ! Q!0A "
Units of C:1 farad = 1 F ! 1 C/V
C geometric property(of any two electrodes)
Capacitors in Parallel• same
• same charge Q
Capacitors in Series
!Vc!
Ceq = !Q!VC
= Q1+Q2!VC
= Q1!VC
+ Q1!VC
1Ceq
= !VCQ = !V1+!V2
Q
= !V1Q + !V2
Q
Circuit analysis
• combine elements into single equivalent; reverse process to calculate for each element
Energy Stored in Capacitor (Electric Field)• Potential energy of d q + capacitor increases by
• total energy transferred from battery to capacitor:
• like spring ( ): discharged/released, potential to kinetic...
• Energy stored in E (real!):
dU = dq!V = qdqC
UC = 1C
! Q0 qdq = Q2
2C = 12C (!VC)2
using !VC = Ed and C = !0A/d, UC = !02 (Ad) E2
uE = energy storedvolume stored in = Uc
Ad = !02 E2
1/2k (!x)2
Chapter 31 (Fundamentals of Circuits)• understand fundamental principles of electric circuits; direct
current (DC): battery’s potential difference, currents constant
• resistors: circuit elements with resistance larger than wires used to limit current
Resistors and Ohm’s law
(cause and effect)
Ohmic and Nonohmic materials; Ideal Wire
Model
• ideal wires:
• resistors:
• ideal insulators:
R = 0 !
R =! "
I = 0 even if !V != 0
10 to 106!
!V = 0 even I != 0
Circuit Elements and Diagrams
• circuit diagram: logical picture of connections (replace pictures of circuit elements by symbols)