Electric Circuits (Fall 2015) Pingqiang Zhou. Lecture 2 Concepts. 9/24/2015 Reading: Chapter 1. Lecture 2

Transcription

1 Concepts 9/24/2015 Reading: Chapter 1 1

2 Outline Electrical quantities Charge, Current, Voltage, Power and Energy Sign conventions Ideal basic circuit elements I-V characteristics of circuit elements Construction of a circuit model 2

3 SI Units Electrical engineers deal with measurable quantities. We use the International Systems of Units (SI for short) Prefixes on SI units allow for easy relationships between large and small values 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 = i 1 + i 2 Net current = i 1 i 2 6

7 TV Picture Tube Old style cathode Ray Tubes (CRT) are a good example of the flow of electrons A hot filament is the source of electrons Charged plates accelerate and steer a thin stream (beam) of electrons The beam strikes a phosphor coated screen causing light emission 7

8 DC versus (vs.) AC A constant current is called a Direct Current" (DC). Otherwise it s AC (alternating current). Some AC typical waveforms are shown above. Sine waves are the waveforms coming out of an electric outlet. A square wave is the clock signal in a digital circuit. Any time-varying current is known as an AC. Note that the sign of the current does not necessarily have to change (the current does not have to alter direction), as the name implies. 8

9 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 = dw 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 as they move downhill". If the energy is negative, then energy must be supplied externally to move the charges uphill". 9

10 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. Sometimes we don t know the actually polarity of the voltage but we just define a reference direction: By convention, when current flows into the positive terminal of a component, we say the current is positive. Otherwise the current is negative. 10

11 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] 11

12 The Concept of Ground It is common to use the ground symbol, shown above, to simplify electrical circuits. All voltages are implicitly referenced to the ground terminal. In reality, this ground" may have a physical form, such as the earth ground, or chassis on an automobile, or a large conductor plane in an electric circuit. The requirement is that all points connected to ground should be at the same voltage, in other words ground is an equipotential surface. This concept is of course an idealization, since no matter how conductive the ground is made, if enough current flows through the ground, then different points can be at different potentials. But usually this potential difference is smaller than the voltage drops in the circuit elements. [Source: Berkeley] 12

13 Power and Energy Definition: transfer of energy per unit time. p dw dt = dw dq dq dt = v i Power =? Net energy supplied by the source =? 13

14 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. 14

15 Power Calculation Exercise Find the power absorbed by each element: Conservation of energy: Does total power delivered equal total power absorbed? 15

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

23 Circuit Applications of Dependent Sources Dependent sources are good models for some common circuit elements: Transistors: In certain modes of operation, transistors take either a voltage or current input to one terminal and cause a current that is somehow proportional to the input to appear at two other terminals. Operational Amplifiers: Not covered yet, but the basic concept is they take an input voltage and generate an output voltage that is proportional to that. 23

24 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

25 Resistor vs. Resistance It s important to realize that we often use a resistor in a schematic to model the equivalent resistance of many components, which may not be resistors at all. Take for example a loudspeaker, which primarily converts electrical energy into sound (pressure waves). Such a component does not ideally dissipate any power as heat, and yet the power conversion into sound can be represented by an equivalent resistance. Other examples include a light bulb (converts electricity into heat and light), an antenna (which converts electricity into electromagnetic radiation), or an entire house which contains hundreds of individual devices dissipating energy. [Source: Berkeley] 25

26 Linearity Not all resistors obey Ohm s Law. Resistors that do are called linear resistors because their current voltage relationship is always linearly proportional. Variable Potentiometer Diodes and light bulbs are examples of non-linear elements. 26

27 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 _ Passive? Active? -1/active-versus-passive-devices/ 27

28 I-V Characteristic of Ideal Voltage Source a + V ab _ b i +_ v s i=0 i V s >0 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? Repeat V s >0 (1) for i<0 v s release < 0. power; i>0 absorb power What is the I-V characteristic for an ideal wire? [Source: Berkeley] 28

29 I-V Characteristic of Ideal Voltage Source a + V ab _ b i +_ v s i=0 V s <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? V s <0 i>0 release power; i<0 absorb power [Source: Berkeley] 29

30 I-V Characteristic of Ideal Current Source i i + v _ i s 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? V>0 absorb power; V<0 release power [Source: Berkeley] 30

31 I-V Characteristic of Ideal Resistor i a + v _ b i R v Plot the I-V characteristic for R = 1 kw. What is the slope? [Source: Berkeley] 31

32 Short Circuit and Open Circuit Short circuit R = 0 no voltage difference exists all points on the wire are at the same potential. Current can flow, as determined by the circuit Open circuit R = no current flows Voltage difference can exist, as determined by the circuit 32

33 An Ideal Switch When an ideal switch is open (off), the flow of current is interrupted and I 0. When an ideal switch is closed (on), then current flows readily through the switch, but the voltage across the switch is zero, V 0. In a fluid flow analogy, the switch is a valve with only two stages, on" and off". [Source: Berkeley] 33

34 Construction of a Circuit Model - Flashlight Modeling Dry cell v s, Lamp R l Connector R 1, Case R c Circuit model The electrical behavior of each physical component is of primary interest. We need to account for undesired as well as desired electrical effects. Simplifying assumptions should be made wherever reasonable. Flashlight components 34

35 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) 35

36 Summary (cont d) Passive sign convention For a passive device, the reference direction for current through the element is in the direction of the reference voltage drop across the element. 36