Circuit Elements. Electric Circuits

Transcription

1 Circuit Elements Qi Xuan Ghangzhi Building( 广知楼 ) C323 I will be in the office on Monday, Wednesday, and Friday Zhejiang University of Technology September 2015 Electric Circuits 1

2 Structure Voltage and Current Sources Electrical Resistance (Ohm s Law) Construc<on of a Circuit Model Kirchhoff s Laws Analysis of a Circuit Containing Dependent Source Electric Circuits 2

3 Circuit Elements When we speak of Circuit Elements, It is important to differen<ate between the physical device itself and the mathema<cal model which we will use to analyze its behavior in a circuit. We will use the expression circuit element to refer to the mathema&cal model. All the simple circuit elements that we will consider can be classified according to the rela<onship of current through the element to the voltage across the element. Electric Circuits 3

4 Five ideal basic circuit elements Resistor Voltage source Current source Inductor Active elements Capacitor Passive elements Electric Circuits 4

5 Electrical safety I The electrical energy that can actually cause injury is due to electrical current and how it flows through the body. Why, then, does the sign warn of high voltage? Because It is easier to determine voltages than currents. Electric Circuits 5

6 Voltage and Current Sources Ideal voltage source: a circuit element that maintains a prescribed voltage across its terminals regardless of the current flowing in those terminals. Ideal current source: a circuit element that maintains a prescribed current through its terminals regardless of the voltage across those terminals. Electric Circuits 6

7 Independent Sources An independent source establishes a voltage or current in a circuit without relying on voltages or currents elsewhere in the circuit. The value of the voltage or current supplied is specified by the value of the independent source alone. Electric Circuits 7

8 Example #1 Which are valid? Electric Circuits 8

9 Dependent Sources A dependent source establishes a voltage or current whose value depends on the value of a voltage or current elsewhere in the circuit. You cannot specify the value of a dependent source unless you know the value of the voltage or current on which it depends. Four kind of controlled sources, current- controlled current source, CCCS; voltage- controlled current source, VCCS; voltage- controlled voltage source, VCVS; current- controlled voltage source, CCVS. Electric Circuits 9

10 The circuit symbols for (a) An ideal dependent voltage-controlled voltage source; (b) An ideal dependent current-controlled voltage source; (c) An ideal dependent voltage-controlled current source; (d) An ideal dependent current-controlled current source. Electric Circuits 10

11 Example #2 Which are valid? Electric Circuits 11

12 Example #3 For the circuit shown, a) What value of v g is required in order for the interconnec<on to be valid? b) For this value of v g, find the power associated with the 8 A source. Electric Circuits 12

13 SoluGon for Example #3 For a), we have v g = i b /4 = 8/4 = 2(V) For b), we have p = 8v g = 8 ( 2) = 16(W) Electric Circuits 13

14 Electrical Resistance (Ohm s Law) Resistance is the capacity of materials to impede the flow of current or, more specifically, the flow of electric charge. The circuit element used to model this behavior is the resistor. The linear resistor is the simplest passive element. Its symbol and characteris<c are as following: Electric Circuits 14

15 Ohm s Law Left: in the direction of the voltage drop across the resistor Right: in the direction of the voltage rise across the resistor Electric Circuits 15

16 Other Forms of Ohm s Law Current is in the direc<on of the voltage drop across the resistor Current is in the direc<on of the voltage rise across the resistor Conductance: the reciprocal of the resistance, which is symbolized by the leyer G, and is measured in Siemens (S) Electric Circuits 16

17 Power in Different Forms Left: P = vi = (ir)i = i 2 R P = vi = v(v/r) = v 2 /R Right: P = vi = ( ir)i = i 2 R P = vi = v( v/r) = v 2 /R The equa<ons for LeZ and right are iden<cal and demonstrate clearly that, regardless of voltage polarity and current direcgon, the power at the terminals of a resistor is posi<ve. Therefore, a resistor absorbs power from the circuit. What s the expression of power if we use conductance, rather than resistance? See example 2.3 (P.55) Electric Circuits 17

18 Example #4 Electric Circuits 18

19 For a), we have SoluGon for Example #4 R = v g /i g = 1 kv / A = 200 kω p = v g i g = 1000 V A = 5 W For b), we have v g =p/i g = 3 W / A = 40 V R = v g /i g = 40 V / A = Ω p absorbed =p delivered = 3 W For c), we have i g = (p/r) 0.5 = (0.48 W / 300 Ω) 0.5 = 0.04 A = 40mA v g = (pr) 0.5 = (0.48 W 300 Ω) 0.5 = 12 V Electric Circuits 19

20 Construc<on of a Circuit Model Flashlight An ideal switch offers no resistance to the current when it is in the ON state, but it offers infinite resistance to current when it is in the OFF state. Electric Circuits 20

21 In developing a circuit model, the electrical behavior of each physical component is of primary interest: a lamp, a coiled wire, and a metal case. The arrangement of flashlight components Circuit models may need to account for undesired as well as desired electrical effects: light and heat. Modeling requires approxima<on. Electric Circuits 21

22 Example #5 The voltage and current are measured at the terminals of the device illustrated in (a), and the values of v t and i t are tabulated in (b). Construct a circuit model of the device inside the box. Electric Circuits 22

23 SoluGon for Example #5 Plo\ng the voltage as a func<on of the current yields the graph shown in (a). The equa<on of the line in this figure illustrates that the terminal voltage is directly proporgonal to the terminal current, v t =4i t. In terms of Ohm's law, the device inside the box behaves like a 4 Ω resistor. Electric Circuits 23

24 Kirchhoff s Law A node is a point where two or more circuit elements meet. Circuit model for the flashlight Based on Ohm s law: Ohm's law may not be enough to provide a complete solugon! Electric Circuits 24

25 Kirchhoff's current law (KCL): The algebraic sum of all the currents at any node in a circuit equals zero. Kirchhoffs voltage law (KVL): The algebraic sum of all the voltages around any closed path in a circuit equals zero. Reference direc&on is important! KCL: Assign a posi<ve sign to a current leaving a node requires assigning a nega<ve sign to a current entering a node, or vice versa. KVL: As we trace a closed path, assign a posi<ve sign to a voltage rise requires assigning a nega<ve sign to a voltage drop, or vice versa. Electric Circuits 25

26 KCL Circuit model for the flashlight KVL Electric Circuits 26

27 Example #6 Use Kirchhoff's current law (KCL) Electric Circuits 27

28 SoluGon for Example #6 Electric Circuits 28

29 Example #7 Electric Circuits 29

30 SoluGon for Example #7 Electric Circuits 30

31 Example #8 Use Ohm's law and Kirchhoff s laws to find the value of R in the circuit. v R i R i 1 i 2 v 2 Kirchhoff s laws: v R = v 2 = 0 i R i 1 i 2 = 0 Ohm's law: R = v R / i R 24 i 1 = i 2 = v 2 R = 4 Ω Electric Circuits 31

32 Analysis of a Circuit Containing Dependent Sources KCL KVL Electric Circuits 32

33 Example #9 a) Use Kirchhoffs laws and Ohm's law to find the voltage v o as shown in the Figure. b) Show that your solu<on is consistent with the constraint that the total power developed in the circuit equals the total power dissipated. Electric Circuits 33

34 SoluGon for Example #9 By using Kirchhoff s voltage law (KVL), we have Then, by using Ohm s law, we have Please check the power balancing! Electric Circuits 34

35 Electrical Safety Electric Circuits 35

36 Summary Ideal voltage/current sources Independent/dependent sources Resistor Ohm s law In series, closed path Kirchhoff s voltage/current law Electric Circuits 36