Circuit Analysis I (ENGR 2405) Chapter 1 Review: Charge, Current, Voltage, Power

Transcription

1 Circuit Analysis I (ENGR 2405) Chapter 1 Review: Charge, Current, Voltage, Power

2 What is a circuit? An electric circuit is an interconnection of electrical elements. It may consist of only two elements or many more: 2

3 Units When taking measurements, we must use units to quantify values 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 When an amber rod is rubbed with fur, some of the electrons on the atoms in the fur are transferred to the amber:

5 Electric Charge: Water (H2O) molecule can be polarized by electrostatic Induction For example, the water molecule has more positive charges on one side of the molecule and negative charges on the other side. Thus, water can be slightly attracted to a static electric charge. A demonstration of that can be seen in bending a stream of water with a charged plastic comb.

6 Electric Charge:

7 Conductors and Insulators

8 Electric Charge Some materials can become polarized this means that their atoms rotate in response to an external charge. This is how a charged object can attract a neutral one.

9 Electric Charge The electrons in an atom are in a cloud surrounding the nucleus, and can be separated from the atom with relative ease.

10 Electric Charge We find that the total electric charge of the universe is a constant: Electric charge is conserved. Also, electric charge is quantized in units of e. The atom that has lost an electron is now positively charged it is a positive ion The atom that has gained an electron is now negatively charged it is a negative ion

11 21.5 Charge is Quantized Many descriptions of electric charge use terms that might lead you to the conclusion that charge is a substance. Phrases like: Charge on a sphere Charge transferred Charge carried on the electron However, charge is a property of particles, one of many properties, such as mass.

12 Charge is Quantized. Since the days of Benjamin Franklin, our understanding of of the nature of electricity has changed from being a type of continuous fluid to a collection of smaller charged particles. The total charge was found to always be a multiple of a certain elementary charge, e : The value of this elementary charge is one of the fundamental constants of nature, and it is the magnitude of the charge of both the proton and the electron. The value of e is:

13 Charge is Quantized Elementary particles either carry no charge, or carry a single elementary charge. When a physical quantity such as charge can have only discrete values, rather than any value, we say the quantity is quantized. It is possible, For example, to find a particle that has no charge at all, or a charge of +10e, or -6e, but not a particle with a charge of, say, 3.57e.

14 Conductors and Insulators Conductors are materials through which charge can move freely; examples include metals (such as copper in common lamp wire), the human body, and tap water. Nonconductors also called insulators are materials through which charge cannot move freely; examples include rubber, plastic, glass, and chemically pure water. Semiconductors are materials that are intermediate between conductors and insulators; examples include silicon and germanium in computer chips. Superconductors are materials that are perfect conductors, allowing charge to move without any hindrance. The properties of conductors and insulators are due to the structure and electrical nature of atoms. Atoms consist of positively charged protons, negatively charged electrons, and electrically neutral neutrons. The protons and neutrons are packed tightly together in a central nucleus. When atoms of a conductor come together to form the solid, some of their outermost (and so most loosely held) electrons become free to wander about within the solid, leaving behind positively charged atoms ( positive ions).we call the mobile electrons conduction electrons. There are few (if any) free electrons in a nonconductor.

15 Charge Charge is a basic SI unit, measured in Coulombs (C) Counts the number of electrons (or positive charges) present. Charge of single electron is 1.602*10-19 C One Coulomb is quite large, 6.24*10 18 electrons. 15

16 Charge II In the lab, one typically sees (pc, nc, or μc) Charge is always multiple of electron charge Charge cannot be created or destroyed, only transferred. 16

17 Electric Current: Although an electric current is a stream of moving charges, not all moving charges constitute an electric current. If there is to be an electric current through a given surface, there must be a net flow of charge through that surface. Two examples are given. 1. The free electrons (conduction electrons) in an isolated length of copper wire are in random motion at speeds of the order of 106 m/s. If you pass a hypothetical plane through such a wire, conduction electrons pass through it in both directions at the rate of many billions per second but there is no net transport of charge and thus no current through the wire. However, if you connect the ends of the wire to a battery, you slightly bias the flow in one direction, with the result that there now is a net transport of charge and thus an electric current through the wire.

18 Electric Current:

19 Electric Current: The figure shows a section of a conductor, part of a conducting loop in which current has been established. If charge dq passes through a hypothetical plane (such as aa ) in time dt, then the current i through that plane is defined as: The charge that passes through the plane in a time interval extending from 0 to t is: Under steady-state conditions, the current is the same for planes aa, bb, and cc and for all planes that pass completely through the conductor, no matter what their location or orientation. The SI unit for current is the coulomb per second, or the ampere (A):

20 Electric Current, Conservation of Charge, and Direction of Current:

21 Current The movement of charge is called a current Historically the moving charges were thought to be positive Thus we always note the direction of the equivalent positive charges, even if the moving charges are negative. 21

22 Current II Current, i, is measured as charge moved per unit time through an element. i dq dt Unit is Ampere (A), is one Coulomb/second 22

23 DC vs. AC A current that remains constant with time is called Direct Current (DC) Such current is represented by the capital I, time varying current uses the lowercase, i. A common source of DC is a battery. A current that varies sinusoidally with time is called Alternating Current (AC) Mains power is an example of AC 23

24 Direction of current The sign of the current indicates the direction in which the charge is moving with reference to the direction of interest we define. We need not use the direction that the charge moves in as our reference, and often have no choice in the matter. 24

25 Direction of Current II A positive current through a component is the same as a negative current flowing in the opposite direction. 25

26 Electric Potential: The potential energy per unit charge at a point in an electric field is called the electric potential V (or simply the potential) at that point. This is a scalar quantity. Thus, The electric potential difference V between any two points i and f in an electric field is equal to the difference in potential energy per unit charge between the two points. Thus, The potential difference between two points is thus the negative of the work done by the electrostatic force to move a unit charge from one point to the other. If we set U i =0 at infinity as our reference potential energy, then the electric potential V must also be zero there. Therefore, the electric potential at any point in an electric field can be defined to be Here W is the work done by the electric field on a charged particle as that particle moves in from infinity to point f. The SI unit for potential is the joule per coulomb. This combination is called the volt (abbreviated V).

27 Voltage Electrons move when there is a difference in charge between two locations. This difference is expressed at the potential difference, or voltage (V). It is always expressed with reference to two locations 27

28 Voltage II It is equal to the energy needed to move a unit charge between the locations. Positive charge moving from a higher potential to a lower yields energy. Moving from negative to positive requires energy. 28

29 Power in Electric Circuits: In the figure, there is an external conducting path between the two terminals of the battery. A steady current i is produced in the circuit, directed from terminal a to terminal b. The amount of charge dq that moves between those terminals in time interval dt is equal to i dt. This charge dq moves through a decrease in potential of magnitude V, and thus its electric potential energy decreases in magnitude by the amount The power P associated with that transfer is the rate of transfer du/dt, given by The unit of power is the volt-ampere (V A).

30 Energy and Power in Electric Circuits When the electric company sends you a bill, your usage is quoted in kilowatt-hours (kwh). They are charging you for energy use, and kwh are a measure of energy.

31 Power and Energy Voltage alone does not equal power. It requires the movement of charge, i.e. a current. Power is the product of voltage and current p vi It is equal to the rate of energy provided or consumed per unit time. It is measured in Watts (W) 31

32 Passive Sign Convention By convention, we say that an element being supplied power has positive power. A power source, such as a battery has negative power. Passive sign convention is satisfied if the direction of current is selected such that current enters through the terminal that is more positively biased. 32

33 Conservation of Energy In a circuit, energy cannot be created or destroyed. Thus power also must be conserved The sum of all power supplied must be absorbed by the other elements. Energy can be described as watts x time. Power companies usually measure energy in watt-hours 33

34 Circuit Elements Two types: Active Passive Active elements can generate energy Generators Batteries Operational Amplifiers 34

35 Circuit Elements II Passives absorb energy Resistors Capacitors Inductors But it should be noted that only the resistor dissipates energy ideally. The inductor and capacitor do not. 35

36 Ideal Voltage Source An ideal voltage source has no internal resistance. It also is capable of producing any amount of current needed to establish the desired voltage at its terminals. Thus we can know the voltage at its terminals, but we don t know in advance the current. 36

37 Ideal Current Source Current sources are the opposite of the voltage source: They have infinite resistance They will generate any voltage to establish the desired current through them. We can know the current through them in advance, but not the voltage. 37

38 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. 38

39 Dependent Sources A dependent source has its output controlled by an input value. Symbolically represented as a diamond Four types: A voltage-controlled voltage source (VCVS). A current-controlled voltage source (CCVS). A voltage-controlled current source (VCCS). A current-controlled current source (CCCS). 39

40 Dependent Source example The circuit shown below is an example of using a dependent source. The source on the right is controlled by the current passing through element C. 40

41 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. 41

42 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. 42