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Exploring Circuit Elements: Capacitors, Inductors, and Sources

Dive deeper into circuit elements like capacitors and inductors. Understand properties, symbols, and energy storage. Learn about independent and dependent sources, Kirchhoff's laws, and solve practical examples. Enhance your knowledge in circuit theory!

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Exploring Circuit Elements: Capacitors, Inductors, and Sources

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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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