EE-200 Learning Module 2: Atoms, Charges, Voltage, and Current PDF

Learning Module 2 ATOMS, ELECTRICAL CHARGE, VOLTAGE, AND CURRENT INTENDED LEARNING OUTCOMES: After completing this unit, you are expected to: 1. discuss why conductors can conduct electricity while other cannot. 2. define voltage and current and discuss...

Learning Module 2 ATOMS, ELECTRICAL CHARGE, VOLTAGE, AND CURRENT INTENDED LEARNING OUTCOMES: After completing this unit, you are expected to: 1. discuss why conductors can conduct electricity while other cannot. 2. define voltage and current and discuss their sign conventions. 3. solve problems regarding voltage, current, charges, energy. 4. identify various types of voltage sources and current sources. 5. classify the three basic types of materials. 6. explain the difference between dependent and independent voltage and current sources. Matter conductor battery Element semiconductor primary cell compound insulator secondary cell Mixture ion wet cell Molecule cation dry cell Atom anion ampere-hour Proton charge ideal current source dependent current electron coulomb source Structure of Matter Matter – anything that occupies space and has weight. Element – a substance that cannot be decomposed any further by chemical action. Atom – smallest part of an element can be reduced to and still keeping the properties of the element. Valence Electrons – electrons found in the outermost shell (valence shell) or orbit of an atom.  Parts of an atom: Name Charge Mass (kg) Diameter (m) Proton Positive charge: 1.672 x 10-27 1/3 of the +1.602 x 10-19 diameter of coulomb electron Electron Negative charge: 9.107 x 10-31 10-15 - 1.602 x 10-19 coulomb Neutron No charge 1.672 x 10-27 approximately the same as proton Why do some materials such as copper can conduct electricity while others cannot? Lets compare a conductor and an insulator. A conductor is characterized by having 3 or less valence electrons while an insulator has 5 or more valence electrons. Conductor Insulator The electron energy level: Rule: Although all electrons have the same negative charges, not all electrons share the same energy level. The further an electron orbits from the nucleus, the greater its energy. Energy Added Rule: The energy added to a valence shell is distributed among the valence electrons. Thus for a given energy, the more valence electrons, the less energy each will get as in the case of an insulator. While materials with few valence electrons such as conductor can get more energy. Rule. If enough energy is added to an electron, the electron will move out from its orbit and move to the next higher orbit. That is, if enough energy is added to a valence electron, the electron will move out from its atom and becomes a free electron since there is no more higher orbit. Conductor energy Large number of free electrons Insulator energy Very few free electrons Number of Free Electrons of Some Common Materials Silver – 1.68 x 1024 free electrons/cubic inch Copper – 1.64 x 1024 free electrons/cubic inch Aluminum – 1024 free electrons/cubic inch Hard Rubber – 3 free electrons/cubic inch What is the importance of free electrons? Electric current is the rate of flow of free electrons. Without free electrons current is impossible to happen. CLASSIFICATION OF MATERIALS ACCORDING TO CONDUCTIVITY Conductors – are substances or materials used to convey or allow the flow of electric current. -has 3 or less valence electrons Materials Considered as Good Electric Conductors are: 1. Silver 7. Zinc 2. Copper 8. Platinum 3. Gold 9. Iron 4. Aluminum 10. Lead 5. Nickel 11. Tin 6. Brass Semiconductors – are classed below the conductors in their ability to carry current. - has exactly 4 valence electrons Silicon and germanium are semiconductor materials. Insulators – are substances or materials that resist the flow of electric current. - has 5 or more valence electrons Various Kinds of Insulators: 1. Rubber 7. Latex 2. Porcelain 8. Asbestos 3. Varnish 9. Paper 4. Slate 10. Oil 5. Glass 11. Wax 6. Mica 12. Thermoplastic  Electric Charge Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C). A body is said to be charged, if it has either an excess or deficit of electrons from its normal values due to sharing. Coulomb (C) – unit of electric charge which is equivalent to 6.24 x 1018 electrons or protons. - named after the French physicist, Charles A. Coulomb (1736 – 1806). The following points should be noted about electric charge: 1. The coulomb is a large unit for charges. In 1 C of charge, there are 1/(1.602 x 10 18) = 6.24 x 1018 electrons. Thus realistic laboratory values of charges are on the order of pC, nC, or µC. 2. According to experimental observation, the only charges that occur in nature are integral multiples of the electronic charge e = -1.602 x 10-19 C. 3. The law of conservation of charge states that charge can neither be created nor destroyed, only transferred. Thus the algebraic sum of the electric charges in a system does not change.  q = 𝑛𝑒 where q = charge in coulombs for a given number of electrons or protons n = no. of electrons or protons e = charge of an electron or proton = + 1.602 x 10-19 coulomb/proton = - 1.602 x 10-19 coulomb/electron EXAMPLE How many coulombs do 93.75 x 10 16 electrons represent? Solution: q = 𝑛𝑒 q = 93.75 x 1016 electrons x (- 1.602 x 10-19 C/electron) = 0.15 C EXAMPLE How many electrons does it take to make 40 C of charge? Solution: q = 𝑛𝑒 𝑞 n= 𝑒 C −40 n= − 1.602 x 10−19 C/electron = 2.5 x 1014 electrons Potential Difference (Voltage) Potential – the capability of doing work Any charge had the capability of doing work of moving another charge either by attraction or repulsion. The net number of electrons moved in the direction of the positive charge plate depends upon the potential difference between the two charges. Volt (V) – unit of potential difference which is equal to one joule of work done per coulomb of charge. Potential difference in electrical terms is more commonly called voltage (V) and is expressed as energy (W) per unit charge (Q): where: W is expressed in Joules (J) and Q is in coulombs(C). The unit of voltage is the volt, symbolized by V. - named after the Italian physicist, Alessandro C. Volta (1754 – 1827) who invented the first electric battery. Voltage is the pressure from an electrical circuit's power source that pushes charged electrons (current) through a conducting loop, enabling them to do work such as illuminating a light. In brief, voltage = pressure, and it is measured in volts (V). The term recognizes Italian physicist Alessandro Volta (1745-1827), inventor of the voltaic pile— the forerunner of today's household battery. In electricity's early days, voltage was known as electromotive force (emf). This is why in equations such as Ohm's Law, voltage is represented by the symbol E. Example of voltage in a simple direct current (dc) circuit: One volt is the potential difference (voltage) between two points when one joule of energy is used to move one coulomb of charge from one point to the other. We assume that we are dealing with a differential amount of charge and energy, then EXAMPLE If 50 J of energy are available for every 10 C of charge, what is the voltage? Solution: 𝑊 𝑉= 𝑄 50 𝐽 𝑉= = 5V 10 𝐶 EXAMPLE An energy of 20 Joules is required in moving a 2- coulomb charge from point A to B. What is the potential difference between point A and B? Solution: 𝑊 𝑉= 𝑄 20 𝐽 𝑉= = 10 V 2𝐶 The Idea of Electric Potential load Direction of electron flow zinc copper H2SO4 Analogy of Electrical Potential Difference Voltage Sources and Their Symbols Ideal Voltage Source A voltage source which has zero resistance. The Ideal Independent Voltage Source This is a circuit element that maintains a prescribed voltage across its terminals regardless of the current through it. The Ideal Dependent Voltage Source This is a voltage source in which a voltage or a current at some other part of the circuit determines the voltage across its terminals. For a battery + For sources other _ than battery Sources of Voltage 1. The Battery A voltage source is a source of potential energy that is also called electromotive force (emf). The battery is one type of voltage source that converts chemical energy into electrical energy. A voltage exists between the electrodes (terminals) of a battery, as shown by a voltaic cell in the figure. One electrode is positive and the other negative as result of the separation of charges caused by the chemical action when two different conducting materials are dissolved in the electrolyte. Difference Between Cell and a Battery Cell – is composed of two dissimilar metals, which are immersed in a conductive liquid or paste called an electrolyte. (Electrolysis is the process of converting chemical energy to electrical energy). Battery – a combination of cells  Classification of Chemical cells (or battery) a. Primary cells are ordinarily not usable after a certain period of time. After this period of time its chemicals can no longer produce electrical energy. b. Secondary cells can be renewed after they are used, by reactivating the chemical process that is used to produce electrical energy. This reactivation is known as charging.  Classification of Cells According to Type of Chemicals Used: a. Wet Cell – uses liquid chemicals b. Dry Cell – contains a chemical paste  Types of Primary and Secondary Cells Cell Name Open Circuit Voltage Cell Type Carbon-zinc 1.5 V Primary Alkaline Primary Zinc-chloride 1.5 V Primary Zinc air cells Manganese-zinc 1.5 V Primary or Secondary Mercury-oxide 1.35 V Primary Silver-oxide 1.5 V Primary Lithium 3.0 V Primary Rechargeable alkaline Secondary Nickel metal hydride Lead-acid 2.1 V Secondary Nickel-cadmium 1.25 V Secondary Nickel-iron 1.2 V Secondary Nickel ion Secondary Lead-acid Secondary Silver-zinc 1.5 V Secondary Silver-cadmium 1.1 V Secondary  Sizes for Popular Types of Dry Cells Size Height (inch) Diameter (inch) D 2¼ 1¼ C 1¾ 1 AA 1 7/8 9/16 AAA 1¾ 3/8 Ampere-Hour Rating of Secondary Cells The capacity of a battery composed of lead-acid cells is given by an ampere-hour rating. A 60- ampere hour battery could theoretically deliver 60 amperes for 1 hour, 30 amperes for 2 hours, or 15 amperes for 4 hours. However, this is an approximate rating dependent upon the rate of discharge and the operating temperature of the battery. The normal operating temperature is considered to be 80 F. 2. The Electronic Power Supply 3. The Solar Cell 4. The Generator  Assignment No. 2 TYPES OF PRIMARY AND SECONDARY CELLS AND THEIR USES Cell Name Open Circuit Voltage Cell Type Carbon-zinc 1.5 V Primary Alkaline Primary Zinc-chloride 1.5 V Primary Zinc air cells Manganese-zinc 1.5 V Primary or Secondary Mercury-oxide 1.35 V Primary Silver-oxide 1.5 V Primary Lithium 3.0 V Primary Rechargeable alkaline Secondary Nickel metal hydride Lead-acid 2.1 V Secondary Nickel-cadmium 1.25 V Secondary Nickel-iron 1.2 V Secondary Nickel ion Secondary Lead-acid Secondary Silver-zinc 1.5 V Secondary Silver-cadmium 1.1 V Secondary Electric Current: Charge in Motion Random motion of free electrons in a material when there is no. When a potential difference between two charges forces a third charge to move, the charge in motion is called an electric current. _ + Electrons flow from negative to positive when a voltage is applied across a conductive material. The movement of free electrons from the negative end of the material to the positive end is the electrical current, symbolized by I. Electrical current is defined as the rate of flow of electrons in a conductive material. Current is measured by the number of electrons (amount of charge, Q) that flows past a point in a unit of time: Q I = t where: I is the current, Q is the charge of the electrons, and t is the time. Ampere (A) – unit of charge flow equal to one coulomb of charge past a given point in one second. -named after the French physicist and mathematician Andre M. Ampere (1175 – 1836) If there a non-linear relationship between charge and time, the current is dq(t) i(t) =. dt. and q t = ‫ ׬‬i t dt Electric current is the time rate of change of charge, measures in amperes (A). EXAMPLE Ten coulombs of charge flow past a given point in a wire in 2 s. What is the current? Solution: 𝑄 𝐼= 𝑡 10 𝐶 𝐼= = 5A 2𝑠 EXAMPLE How many electrons pass a given point in 40 seconds in a conductor carrying 10 amps? Solution: 𝑄 = 𝐼𝑡 𝐶 𝑄 = 10 40𝑠 = 400 𝐶 𝑠 𝑞 𝑛= 𝑒 400 𝐶 𝑛= 1.602 𝑥 10−19 𝐶 /𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 𝑛 = 25 x 1020 electrons EXAMPLE Example Determine the current flowing through an element if the charge flow is q(t) = (3t + 8) mC Solution: dq(t) i(t) = dt d(3t+8) i(t) = dt 3dt = +0 dt i t = 3 𝑚𝐴 EXAMPLE Example Determine the total charge transferred over 1 the time interval of 0  t  10 s when i(t) = t. 2 Solution: t2 q t = න i t dt t1 10 1 q t = න t dt 0 2 q(t)= 25 C EXAMPLE The charge that enters the BOX is shown below. Calculate and sketch the current flowing into the BOX between 0 and 10 milliseconds. C1 E BOX 12 V 1µF q(t) (mC) 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 t (ms) -1 -2 -3 Solution: Recall that current is related to charge dq(t) by i(t) =. The current is equal to the dt slope of the charge waveform. 𝐢 𝐭 =𝟎 𝟎  𝐭  𝟏 𝐦𝐬 𝟑 𝐱 𝟏𝟎−𝟑 − 𝟏 𝐱 𝟏𝟎−𝟑 𝟏  𝐭  𝟐 𝐦𝐬 𝐢 𝐭 = = 𝟐𝐀 𝟐 𝐱 𝟏𝟎−𝟑 − 𝟏 𝐱 𝟏𝟎−𝟑 𝐢 𝐭 = 𝟎 𝟐  𝐭  𝟑 𝐦𝐬 −𝟐 𝐱 𝟏𝟎−𝟑 − 𝟑 𝐱 𝟏𝟎−𝟑 𝟑  𝐭  𝟓 𝐦𝐬 𝐢 𝐭 = 𝟓 𝐱 𝟏𝟎−𝟑 − 𝟑 𝐱 𝟏𝟎−𝟑 = −𝟐. 𝟓 𝐀 𝐢 𝐭 = 𝟎 𝟓  𝐭  𝟔 𝐦𝐬 𝟐 𝐱 𝟏𝟎−𝟑 − (−𝟐 𝐱 𝟏𝟎−𝟑) 𝟔  𝐭  𝟗 𝐦𝐬 𝐢 𝐭 = 𝟗 𝐱 𝟏𝟎−𝟑 − 𝟔 𝐱 𝟏𝟎−𝟑 = 𝟏. 𝟑𝟑 𝐀 𝐢 𝐭 = 𝟎 𝐭  𝟗 𝐦𝐬 EXAMPLE The current in a conductor varies as follows: during the first 2 sec there is a linear change from zero to 5 amp; during the next 4 sec the current is constant at 5 amp; during the third period of 6 sec the current decreases linearly to 2 amp. Determine the total charge transferred in the elapsed time of 12 sec. i (A) 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 t (s) Solution: Since q(t)= ‫׬‬i(t)dt. Charge is equal to the area bounded by the x and y axes. 1 1 q= (2)(5)+ (4)(5)+ (6)(5+2) =46 C 2 2 Current Sources Ideal Current Source a current source which has a very high resistance. The Ideal Independent Current Source This is a circuit element that maintains a prescribed current in its terminals regardless of the voltage across it. I The Ideal Dependent Current Source This is a current source in which either a voltage or a current at some other part of the circuit determines the current I in its terminals. The Conventional Direction of Current and Electron Flow Conventional Direction of Current Electron Flow Conventions of Voltage vab = - vba. Since the polarity is reversed the value becomes –12 V. The current becomes –3 A because the direction of the original current is reversed. 3A -3 A