Capacitors; Inductors; Dependent Sources; KVLEnergy Storage ElementsCapacitanceSlide 4CapacitorInductanceSlide 7InductorIndependent vs. Dependent SourcesSlide 10Slide 11Kirchhoff’s LawsKVL (Kirchhoff’s Voltage Law)KVL PolarityElectrical Analogies (Physical)Class ExamplesLect2 EEE 202 1Capacitors; Inductors; Dependent Sources; KVLDr. HolbertJanuary 16, 2008Lect2 EEE 202 2Energy Storage Elements•Capacitors store energy in an electric field•Inductors store energy in a magnetic field•Capacitors and inductors are passive elements:–Can store energy supplied by circuit–Can return stored energy to circuit–Cannot supply more energy to circuit than is storedLect2 EEE 202 3Capacitance•Capacitance occurs when two conductors (plates) are separated by a dielectric (insulator)•Charge on the two conductors creates an electric field that stores energy – – – – – – – – – – + + + + + + + +Lect2 EEE 202 4Capacitance•The voltage difference between the two conductors is proportional to the charge:q = C v , thereforei = dq/dt = C dv/dt•The proportionality constant C is called capacitance.–Units of Farads (F) = Coulomb/Volt–For two parallel plates: C = ε A / dLect2 EEE 202 5CapacitordttdvCti)()( tdxxiCtv )(1)(i(t)+–v(t)TherestofthecircuitCLect2 EEE 202 6Inductance•Inductance occurs when current flows through a (real) conductor•The current flowing through the conductor sets up a magnetic field that is proportional to the current: Φ I•The voltage difference across the conductor is proportional to the rate of change of the magnetic field: V dΦ/dtLect2 EEE 202 7Inductance•The voltage difference across the inductor is proportional to the rate of change of the current: V dΦ/dt dI/dt•The proportionality constant is called the inductance, denoted L, such that V = L di/dt•Units of Henrys (H) = V·s/ALect2 EEE 202 8InductordttdiLtv)()( i(t)+–v(t)TherestofthecircuitLtdxxvLti )(1)(Lect2 EEE 202 9Independent vs. Dependent SourcesAn independent source (voltage or current) may be DC (constant) or time-varying, but does not depend on other voltages or currents in the circuitThe dependent source magnitude is a function of another voltage or current in the circuit+–Lect2 EEE 202 10Dependent Voltage Sources+–6VxVoltage-Controlled Voltage Source (VCVS)6000IxCurrent-Controlled Voltage Source (CCVS)+–Lect2 EEE 202 11Dependent Current Sources0.006VxVoltage-Controlled Current Source (VCCS)6IxCurrent-Controlled Current Source (CCCS)Lect2 EEE 202 12Kirchhoff’s Laws•Kirchhoff’s Current Law (KCL)–sum of all currents entering a node is zero–sum of currents entering node is equal to sum of currents leaving node•Kirchhoff’s Voltage Law (KVL)–sum of voltages around any loop in a circuit is zeroLect2 EEE 202 13KVL (Kirchhoff’s Voltage Law)The sum of voltages around a loop is zero:Analogy: pressure drop through pipe loop0)(1njjtvv1(t)++––v2(t)v3(t)+–Lect2 EEE 202 14KVL Polarity•A loop is any closed path through a circuit in which no node is encountered more than once•Voltage Polarity Convention–A voltage encountered + to – is positive–A voltage encountered – to + is negativeLect2 EEE 202 15Electrical Analogies (Physical)Electric HydraulicBase quantity Charge (q) Mass (m)Flow variable Current (I) Fluid flow (G)Potential variable Voltage (V) Pressure (p)Power P = I V P = G pJunction/Node Law KCL: Σ I = 0 Σ G = 0Loop Law KVL: Σ V = 0 Σ Δp = 0Lect2 EEE 202 16Class Examples•Drill Problems P1-5, P1-9, P1-7, P1-10–While working these problems, we shall define the terms ‘loop’ and
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