hing/fall16/electric_circuits.html

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1 hing/fall16/electric_circuits.html

2 Circuit Terminology & Kirchhoff s Laws 9/14/2016 Reading: Chapter 1&2&3 2

3 Outline Circuit Terminology Charge, Current, Voltage, Power and Energy Ideal basic circuit elements Sign conventions I-V characteristics Kirchhoff s Laws KCL KVL 3

4 Electric Charge Electrical effects are due to Separation of charge -> electric force Macroscopically, most matter is electrically neutral most of the time Exceptions: clouds in a thunderstorm, people on carpets in a dry weather, plates of a charged capacitor, etc. Microscopically, matter is full of electric charges Electric charge exists in discrete quantities, integral multiples of the electronic charge *10-19 Coulomb. 4

5 Etymology The word electric is derived from the Greek elektron (Latin electrum) denoting amber. It was discovered in ancient times that when amber is rubbed, it attracts feathers, dried leaves, etc. This is due to the amber becoming charged (discovered much later). These are the roots of our subject. [Source: Berkeley] 5

6 Electric Current Charges in motion -> electric flow (current) The current flowing through a surface can be defined as I = Net Charge crossing surface in time t t = dq dt Net current = Net current = 6

7 TV Picture Tube Old style cathode Ray Tubes (CRT) are a good example of the flow of electrons 7

8 Voltage (= Electric Potential) The voltage difference V AB between A and B is the amount of energy gained or lost per unit of charge in moving between two points. v = de dq Voltage is a relative quantity. An absolute voltage is meaningless and usually is implicitly referenced to a known point in the circuit (ground) or in some cases a point at infinity. If a total charge of q is moved from A B, the energy required is E = q V AB, V AB V A V B If the energy is positive, then energy is lost by the charges. Why? 8

9 Voltage across a Component In electrical circuits, the path of motion is well defined by wires/circuit components (also known as elements). We usually label the terminals of a component as positive and negative to denote the voltage drop across the component. 9

10 Power and Energy Definition: transfer of energy per unit time. p de dt = de dq dq dt = v i Power =? Net energy supplied by the source =? [Source: Berkeley] 10

11 Outline Circuit Terminology Charge, Current, Voltage, Power and Energy Ideal basic circuit elements Sign conventions I-V characteristics Kirchhoff s Laws KCL KVL 11

12 The Ideal Basic Circuit Element + v _ i Polarity reference for voltage can be indicated by plus and minus signs. Reference direction for the current is indicated by an arrow. Attributes: Two terminals (points of connection) Mathematically described in terms of current and/or voltage Cannot be subdivided into other elements 12

13 Sign Convention A problem like Find the current or Find the voltage is always accompanied by a definition of the direction: i - v + In this case, if the current turns out to be 1 ma flowing to the left, we would say i =?. In order to perform circuit analysis to determine the voltages and currents in an electric circuit, you need to specify reference directions. By convention, when current flows into the positive terminal of a component, we say the current is positive. Otherwise the current is negative. [Source: Berkeley] 13

14 Sign Convention Example Suppose you have an unlabelled battery and you measure its voltage with a digital voltmeter (DVM). It will tell you the magnitude and sign of the voltage. a b DVM With this circuit, you are measuring v ab. The DVM indicates 1.401, so v a is lower than v b by V. Which is the positive battery terminal? Note that we have used the ground symbol ( ) for the reference node on the DVM. Often it is labeled C for common. [Source: Berkeley] 14

15 Passive Sign Convention (for Power) i p = vi i i p = -vi i + v v + + v v + If p > 0, power is absorbed by the element. electrical energy into heat (resistors in toasters), light (light bulbs), or acoustic energy (speakers); by storing energy (charging a battery). If p < 0, power is extracted from the element. 15

16 Power Calculation Example Find the power absorbed by each element: Conservation of energy: Does total power delivered equal total power absorbed? [Source: Berkeley] 16

17 Circuit Elements 5 ideal basic circuit elements: voltage source current source resistor inductor capacitor active elements, capable of generating electric energy passive elements, incapable of generating electric energy Many practical systems can be modeled with just sources and resistors. The basic analytical techniques for solving circuits with inductors and capacitors are similar to those for resistive circuits. 17

18 Ideal Voltage Source Circuit element that maintains a prescribed voltage across its terminals, regardless of the current flowing in those terminals. Voltage is known, but current is determined by the circuit to which the source is connected. The voltage can be either independent or dependent on a voltage or current elsewhere in the circuit, and can be constant or time-varying. Device symbols: v s +_ v s =m v x +_ v s =r i x +_ independent voltage-controlled current-controlled 18

19 Electrical Sources An electrical source is a device that is capable of converting non-electric energy to electric energy and vice versa. Examples: battery: chemical electric dynamo (generator/motor): mechanical electric (Ex. gasoline-powered generator, Bonneville dam) Electrical sources can either deliver or absorb power. 19

20 Ideal Current Source Circuit element that maintains a prescribed current through its terminals, regardless of the voltage across those terminals. Current is known, but voltage is determined by the circuit to which the source is connected. The current can be either independent or dependent on a voltage or current elsewhere in the circuit, and can be constant or time-varying. Device symbols: i s i s =a v x i s =b i x independent voltage-controlled current-controlled 20

21 Ideal Sources Both the voltage and current source ideally can generate infinite power. They are also capable of absorbing power from the circuit. It is important to remember that these sources do have limits in reality: Voltage sources have an upper current limit. Current sources have an upper voltage limit. 21

22 Exercise Calculate the power supplied or absorbed by each element in the following figure. 22

23 Electrical Resistance/Conductance Resistance: the ratio of voltage drop and current. The circuit element used to model this behavior is the resistor. R Circuit symbol: The current flowing in the resistor is proportional to the voltage across the resistor: v = i R (Ohm s Law) Conductance is the reciprocal of resistance G = 1 R = i v Werner von Siemens

24 Current vs. Voltage (I-V) Characteristic Voltage sources, current sources, and resistors can be described by plotting the current (i) as a function of the voltage (v). i + v _ 24

25 I-V Characteristic of Ideal Voltage Source a + V ab _ i +_ v s i=0 i v b Plot the I-V characteristic for v s > 0. For what values of i does the source absorb power? For what values of i does the source release power? Repeat (1) for v s < 0. What is the I-V characteristic for an ideal wire? [Source: Berkeley] 25

26 I-V Characteristic of Ideal Voltage Source a + V ab _ b i +_ v s i=0 i v Plot the I-V characteristic for v s < 0. For what values of I does the source absorb power? For what values of i does the source release power? [Source: Berkeley] 26

27 I-V Characteristic of Ideal Current Source i i + v _ i s i=0 v Plot the I-V characteristic for i s > 0. For what values of v does the source absorb power? For what values of v does the source release power? [Source: Berkeley] 27

28 I-V Characteristic of Ideal Resistor i a i + v _ R i=0 v b Plot the I-V characteristic for R = 1 kw. What is the slope? [Source: Berkeley] 28

29 Outline Circuit Terminology Charge, Current, Voltage, Power and Energy Ideal basic circuit elements Sign conventions I-V characteristics Kirchhoff s Laws KCL KVL 29

30 Terminology: Nodes, Branches and Loops Node: A point where two or more circuit elements are connected. Branch: A path that connects two nodes. Loop: Any closed path in a circuit. [Source: MIT] 30

31 Kirchhoff s Laws Ohm s law is not sufficient for circuit analysis Kirchhoff s laws complete it. Gustav Robert Kirchhoff Kirchhoff s Current Law (KCL): The algebraic sum of all the currents entering any node in a circuit equals zero. Why? 31

32 A Major Implication of KCL KCL tells us that all of the elements that are connected in series carry the same current. Current entering node = Current leaving node 32

33 Generalization of KCL The sum of currents entering/leaving a closed surface is zero. Circuit branches can be inside this surface, i.e. the surface can enclose more than one node! i 2 i 3 This could be a big chunk of a circuit, e.g. a black box i 4 i 1 33

34 Generalized KCL Examples 50 ma 5mA 2mA i i 34

35 Notation: Node and Branch Voltages a R 1 b +_ v s R 2 c REFERENCE NODE Use one node as the reference (the common or ground node) label it with a symbol. The voltage drop from node x to the reference node is called the node voltage v x. The voltage across a circuit element is defined as the difference between the node voltages at its terminals. 35

36 Kirchhoff s Voltage Law (KVL) The algebraic sum of all the voltages around any loop in a circuit equals zero. Why? 36

37 KVL Example Three closed paths: + v a v v b v 3 a b c v c Path 1: Path 2: Path 3: 3 37

38 A Major Implication of KVL KVL tells us that any set of elements which are connected at both ends carry the same voltage. We say these elements are connected in parallel. + v a _ + v b _ 38

39 Series Resistors 39

40 Voltage Division 40

41 When can the Voltage Divider Formula be Used? I I V SS + R 1 R 2 R 3 + V 2 V SS + R 1 R 2 R 3 + V 2 R 4 R 4 R 5 41

42 Parallel Resistors 42

43 Current Division 43

44 Summary Current = rate of charge flow, i = dq/dt Voltage = energy per unit charge created by charge separation Power = energy per unit time Ideal Basic Circuit Elements two-terminal component that cannot be sub-divided described mathematically in terms of its terminal voltage/current An ideal voltage source maintains a prescribed voltage regardless of the current in the device. An ideal current source maintains a prescribed current regardless of the voltage across the device. A resistor constrains its voltage and current to be proportional to each other: v = ir (Ohm s law) 44

45 Summary KCL and KVL N n 1 i n 0 M m 1 v m 0 45

46 New Content for the Discussion Session Dependent sources (Example: Transistor) Ohm s Law: Nonlinearity Voltmeter/Ammeter Wye-Delta Transformations 46

47 Announcements Next lecture Sept. 19 th, Monday Reading Ch. 4 Reminders HW1 will be out on next week. Lab starts from next week. Guide for Lab1 will be online later today. 47