Download • Capacitance • Combinations of capacitors (series and parallel

Lecture 36
• Capacitance
• Combinations of capacitors (series and parallel)
• Energy stored in capacitor (electric field)
• start chapter 31 (Fundamentals of Circuits)
Capacitance
∆Vc = 0
∆Vwire = 0
V = Ed; E =
Q
C ≡ !0 A ⇒
Q
!0 A ;
Units of C:
1 farad = 1 F ≡ 1 C/V
C geometric property
(of any two electrodes)
Combinations...
Capacitors in Parallel
•
same ∆Vc ⇒
∆Q
Ceq = ∆VC =
=
Q1
∆VC
+
Q1 +Q2
∆VC
Q1
∆VC
Capacitors in Series
•
same charge Q
1
Ceq
=
∆VC
Q
=
∆V1
Q
=
+
∆V1 +∆V2
Q
∆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 dU = dq∆V =
•
•
like spring (1/2k (∆x)2): discharged/released, potential to kinetic...
qdq
C
total energy transferred from battery to capacitor:
!
Q
2
Q2
1
1
UC = C 0 qdq = 2C = 2 C (∆VC )
Energy stored in E
(real!): using ∆VC = Ed and C = !0 A/d, UC =
energy stored
uE =
=
volume stored in
Uc
Ad
=
!0
2
(Ad) E 2
!0 2
2 E
•
Chapter 31 (Fundamentals of Circuits)
understand fundamental principles of electric circuits; direct
current (DC): battery’s potential difference, currents constant
Resistors and Ohm’s law
(cause and effect)
•
resistors: circuit elements with resistance
larger than wires used to limit current
Ohmic and Nonohmic
materials; Ideal Wire
Model
•
•
•
ideal wires: R = 0 ⇒
∆V = 0 even I != 0
resistors:
10 to 106 Ω
ideal insulators:
R=∞⇒
I = 0 even if ∆V != 0
Circuit Elements and Diagrams
•
circuit diagram: logical picture of connections (replace
pictures of circuit elements by symbols)