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Capacitors; Inductors; Dependent Sources; KVL

Capacitors; Inductors; Dependent Sources; KVL. Dr. Holbert January 16, 2008. Energy 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

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Capacitors; Inductors; Dependent Sources; KVL

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  1. Capacitors; Inductors; Dependent Sources; KVL Dr. Holbert January 16, 2008 EEE 202

  2. Energy 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 stored EEE 202

  3. Capacitance • Capacitance occurs when two conductors (plates) are separated by a dielectric (insulator) • Charge on the two conductors creates an electric field that stores energy + + + + + + + + – – – – – – – – – – EEE 202

  4. Capacitance • The voltage difference between the two conductors is proportional to the charge: q = C v , therefore i = 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 / d EEE 202

  5. The rest of the circuit + i(t) v(t) C – Capacitor EEE 202

  6. Inductance • 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/dt EEE 202

  7. Inductance • 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/A EEE 202

  8. i(t) The rest of the circuit + L v(t) – Inductor EEE 202

  9. + – Independent vs. Dependent Sources An independent source (voltage or current) may be DC (constant) or time-varying, but does not depend on other voltages or currents in the circuit The dependent source magnitude is a function of another voltage or current in the circuit EEE 202

  10. Dependent Voltage Sources 6Vx 6000Ix + – + – Voltage-Controlled Voltage Source (VCVS) Current-Controlled Voltage Source (CCVS) EEE 202

  11. Dependent Current Sources 0.006Vx 6Ix Voltage-Controlled Current Source (VCCS) Current-Controlled Current Source (CCCS) EEE 202

  12. Kirchhoff’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 zero EEE 202

  13. KVL (Kirchhoff’s Voltage Law) The sum of voltages around a loop is zero: Analogy: pressure drop through pipe loop + – + v2(t) + – v1(t) v3(t) – EEE 202

  14. KVL 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 negative EEE 202

  15. Electrical Analogies (Physical) EEE 202

  16. Class Examples • Drill Problems P1-5, P1-9, P1-7, P1-10 • While working these problems, we shall define the terms ‘loop’ and ‘mesh’ EEE 202

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