Chapter 1

1. Chapter 1 Circuit Elements and Variables

2. What is Electric Circuit? • An electric circuit is an interconnection of electrical elements • Example: Consists of 3 basic elements: battery, lamp, connecting wires. • When the wires are connected properly, the circuit is said to be closed and the lamp will light. When the wires are disconnected, the circuit is said to be open.

3. Circuit Diagram

4. Basic Electric Concept • Review SI unit (International Systems of Unit) • Know the definition of basic electrical quantities : charge, current, voltage, power & energy • Know the symbols and definitionof the elements of the circuit: passive and active elements & independent and dependent sources • To understand some fundamentals laws and basic network to determine the values of electric circuit variables: Ohm’s Law, nodes, branches, loops & Kirchoff’s Law

5. Review SI Units (1) SI: International System of Unit is used by all the major engineering societies and most engineers throughout the world.

6. Review SI Units(2) Standardized prefixes to signify powers of 10

7. Basic Electric Concept • Review SI unit (International Systems of Unit) • Know the definition of basic electrical quantities : charge, current, voltage, power & energy • Know the symbols and definitionof the elements of the circuit: passive and active elements & independent and dependent sources • To understand some fundamentals laws and basic network to determine the values of electric circuit variables: Ohm’s Law, nodes, branches, loops & Kirchoff’s Law

8. Unit, Symbol and Definition

9. Charge, Q (C) The charge on one electron is called electronic charge and equivalent to Q of e = - 1.602  10-19 C How many electrons in 1 C? 1 C = 1 / 1.602  10-19 = 6.24 x 1018 electrons

10. Current, I (A) Currentis the movement of charge in a specified direction. dQ Charge C/s Current = I (A) = dt Time 2 common types of current: Direct current (DC) Alternating current (AC)

11. Voltage, V (v) Voltage (or potential difference) isthe energy required to move a unit charge through an element It is a potentialenergy difference between two points, a and b Energy dW Voltage = vab= dQ Charge

12. + i i + v v – – Power, P (W) Poweris the time rate of expending or absorbing energy. Energy dW Power = P = dt Time P = +viP= –vi absorbing power supplying power

13. Energy, W (J) • Energy is the capacity to do work, measured in joules (J).

14. Basic Electric Concept • Review SI unit (International Systems of Unit) • Know the definition of basic electrical quantities : charge, current, voltage, power & energy • Know the symbols and definition of the elements of the circuit: passive and active elements & independent and dependent sources • To understand some fundamentals laws and basic network to determine the values of electric circuit variables: Ohm’s Law, nodes, branches, loops & Kirchoff’s Law

15. Circuit Elements • Active elements • capable of generating electric energy • Example : generators, batteries, operational amplifier, voltage and current sources • Passive elements • incapable of generating electric energy • Example : resistor, inductor, capacitor Active and Passive Elements

16. Independent Source AC DC Current (arrow) Voltage (+/- sign)

17. Dependent Source • A dependent source is an active element in which the source quantity is controlled by another voltage or current. • They have four different types: • VCVS: Voltage-controlled voltage source • CCVS: Current-controlled voltage source • VCCS: Voltage-controlled current source • CCCS: Current-controlled current source

18. Dependent Source (Diamond shape) Current (arrow) Voltage (+/- sign)

19. Example of sources Current controlled voltage source, V =10 i Current controlled current source, Is =10.2 I Independent voltage source V =20 V

20. Basic Electric Concept • Review SI unit (International Systems of Unit) • Know the definition of basic electrical quantities : charge, current, voltage, power & energy • Know the symbols and definitionof the elements of the circuit: passive and active elements & independent and dependent sources • To understand some fundamentals laws and basic network to determine the values of electric circuit variables: Ohm’s Law, nodes, branches, loops & Kirchoff’s Law

21. Ohms Law • Ohm’s law states that the voltage across a resistor is directly proportional to the current I flowing through the resistor. • Two extreme possible values of R: R = 0 : short circuit R =  : open circuit.

22. Short Circuit R = 0 , no voltage difference exists, thus V = 0 V, but current still can flow.

23. Open circuit R =  , no current flows .Voltage difference can exist, as determined by the circuit

24. Conductance & Power • Conductance is a measure of the ability of an element to conduct electric current • Inverse of resistance • The units is Siemens (S) or mhos • Power dissipated by resistor:

25. Example 1 • In the circuit, calculate the current I, the conductance G, and the power P.

26. Example 2 • In the circuit, calculate the voltage V, the conductance G, and the power P.

27. Branches • A branch represents a single element such as a voltage source or a resistor. • In other words, a branch represents any elementswhich has two terminals. 4 1 3 2

28. Should we consider it as one branch or two branches? Exercise

29. Nodes • A node is the point of connection between two or more branches. • A node usually indicated by a dot in a circuit. • If a short circuit (no element between dots), the multiple dots constitute as a single nodes. • How many branches connected to node a, b and c?

32. Loops • A loop is any closed path in a circuit.

33. Relation of branches, nodes and loops • A network with b branches, n nodes, and l independent loops will satisfy the fundamental theorem of network topology:

34. Example 3 How many branches, nodes and loops are there? Does it satisfy b = l + n -1?

35. Kirchhoff Law • Gustav Robert Kirchhoff (1824–1887) • Models relationship between: • circuit element currents (KCL) • circuit element voltages (KVL) • Introduce two laws: • Kirchhoff Current Law (KCL) • Kirchhoff Voltage Law (KVL)

36. Kirchhoff’s Current Laws (KCL) • Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero.

37. Kirchhoff’s Current Laws (KCL) • Convention sign for current entering and leaving node: current entering node = + i current leaving node = - i • According to KCL, for any node: • Without the sign (+Ve or -Ve), the formula of KCL can be written as: Current entering node = current leaving node (What goes in, must comes out) N = number of branches connected to the nodes in = nth current entering (+ i) or leaving (- i) the node

38. Example of KCL (1) Node A • 2 options: Current entering = current leaving Current leaving node, (-i) Current entering node, (+i)

39. Example of KCL (2) Node a IT : Leaving node a (-Ve) I1 : Entering node a (+Ve) I2: Leaving node a (-Ve) I3: Entering node a (+Ve)

40. Kirchhoff’s Voltage Laws (KVL) • Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero.

41. Kirchhoff’s Voltage Law (KVL) For any circuit loop: Convention sign for voltage inside loop (clockwise or anticlockwise direction): • If the positive terminal of voltage is met first: +V • If the negative terminal of voltage is met first: -V Without the +/- sign, KVL formula can be written as Sum of voltage drops = sum of voltage rises M = number of voltages in the loop vm = mth voltage

42. Example of KVL +V Voltage drop +V Voltage drop -V Voltage rise -V Voltage rise +V Voltage drop

44. Example 4 • Find v1 and v2 using KVL and Ohm’s Law.

45. Example 5 • Find v1, v2 and v3 using Ohm’s Law KCL and KVL.

46. Example 6 • Determine vo and I in the circuit