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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)