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)