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Capacitor * What is a capacitor? * Capacitance * Properties Inductor * What is an inductor?

Lecture 2. More on Circuit Elements &KCL. Capacitor * What is a capacitor? * Capacitance * Properties Inductor * What is an inductor? * Inductance * Properties Dependent sources * 2 types of independent sources & symbols * 4 types of dependent sources & symbols KVL.

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Capacitor * What is a capacitor? * Capacitance * Properties Inductor * What is an inductor?

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  1. Lecture 2. More on Circuit Elements &KCL • Capacitor * What is a capacitor? * Capacitance * Properties • Inductor • * What is an inductor? • * Inductance • * Properties • Dependent sources • * 2 types of independent sources & symbols * 4 types of dependent sources & symbols • KVL

  2. Capacitor • A passive circuit element that can store charge (energy) • Capacitance (C): describes capacity of storing charge C = q/V Unit: 1 Fara (or F) = 1 Coulomb/Volt Capacitors everywhere Some examples of capacitors

  3. Parallel-Plate Capacitor • Two conductive parallel plates with a separation usually filled with a certain dielectric material. C = e0kA/d where e0=8.85x10-12 F*m; k is dielectric constant, A is area of the plate and d the separation between the plates. Parallel-plate capacitor

  4. The rest of the circuit + i(t) v(t) – Capacitor in Circuits What is V(t0)? Energy stored:

  5. i(t) 1A 2s -1A t 1s Example i(t) The rest of the circuit + 0.2F v(t) v(t)=?wc(t)=? -

  6. v(t) 5V 2s 1s t Solution wc(t) 2.5J 2s 1s t

  7. Inductor • A passive circuit element that can store energy in magnetic field • Inductance (L): describes capacity of an element to create a magnetic field flux due to current V = LdI/dt Unit: 1 H = 1 Coulomb/Volt Capacitors everywhere Some examples of capacitors

  8. i(t) The rest of the circuit + H v(t) – Inductor in Circuits Energy stored:

  9. Example The current through a 1H inductor is i(t) = 0.45A cos(2 60 t) Find v(t), p(t), and wL(t)

  10. Solution p(t)=? wL(t)=? Matlab >t=0:0.001:0.1; >i=0.45*cos(2*pi*60*t); >v=-169.7*sin(2*pi*60*t); >plotyy(t,v,t,i)

  11. + – Independent 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 Vs Is Independent voltage source Independent current source 2-types

  12. Dependent Sources The dependent source magnitude is a function of another voltage or current in the circuit 0.006Vx 6Ix 6000Ix 6Vx + – + – Vs Is Voltage-Controlled Voltage Source Current-Controlled Voltage Source Voltage-Controlled Current Source Current-Controlled Current Source 4-types

  13. 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 • What is a node? • A node is a connection point of three or more circuit elements. • Kirchhoff’s Voltage Law (KVL) • sum of voltages around any loop in a circuit is zero • What is a loop or mesh? • A loop or mesh is a closed path that does not encircle any other elements or sources.

  14. KVL (Kirchhoff’s Voltage Law) + – + v2(t) + – v1(t) v3(t) – • The sum of voltages around a loop is zero:

  15. Applying KVL – the Signs • 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

  16. Class Examples • Drill Problems 5, 9, 7, 10

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