4 Electrical Quantities and Ohm s Law

Ch a pt er 4 Electrical Quantities and Ohm s Law Learning Outcomes Define electric current, voltage, resistance, power, and energy, and list the unit of measurement of each. Identify the essential parts of a circuit and state the purpose of each. In practical situations, you must be able to measure electricity if you want to work with it. This chapter deals with the standard units used for measuring of electric voltage, current, resistance, power, and energy. It also introduces Ohm s law which defines the relationship between voltage, current, and resistance. Calculate different electric values using Ohm s law. State the difference between electron flow and conventional current flow. 27 pet34317_ch04_027-034.indd 27 22/11/12 3:48 PM

Part 1 Current, oltage, and Resistance 4.1 Current The coulomb is a measurement for a quantity of electrons, and the practical unit for an electric charge. One coulomb of charge represents a total charge of 6.24 10 18 (6,240,000,000,000,000,000) electrons. That appears to be a lot, but only because the charge on one electron is so small. Charge in motion is referred to as current. Current is the rate of flow of electrons through a conductor. The letter I (which stands for intensity ) is the symbol used to represent current. Current is measured in amperes (). The term ampere refers to the number of electrons passing a given point in 1 second. If we could count the individual electrons, we would discover that 1 ampere of current is equal to 1 coulomb of charge moving past a given point in 1 second, as illustrated in Figure 4-1. When the electrons begin to flow, the effect is felt instantly all along the conductor similar to the force that can Measurement point 6.24 x 10 18 Figure 4-1 One ampere of current flow. Electrons per second Figure 4-2 Transmission of electrons by impulse. be transmitted through a row of billiard balls, as illustrated in Figure 4-2. The electric current is actually the impulse of electric energy that one electron transmits to another as it changes orbit. The first electron repels the other out of orbit, transmitting its energy to it. The second electron repeats the action, and this process continues through the conductor. lthough the individual electrons travel less than an inch per second, the current effectively travels through the conductor nearly at the speed of light (186,000 miles per second). Because the atoms are close and the orbits overlap, the electron that is freed does not have to travel far to encounter a new orbit. This action is almost instantaneous so that even though the electrons are moving relatively slowly, the electric current travels at almost the speed of light. n instrument called an ammeter is used to measure current flow in a circuit ( Figure 4-3 ). The ammeter is inserted into the path of the current flow, or in series, to measure current. This means the circuit must be opened and the meter leads placed between the two open points. lthough the ammeter measures electron flow in coulombs per second, it is calibrated or marked in amps or amperes. For most practical applications, the term amps is used instead of coulombs per second when referring to the amount of current flow. Prefixes micro 1 ( 1,000,000 ) and milli 1 ( 1,000 ) are used to represent very small amounts of current and kilo (1,000) and mega (1,000,000) to represent very large amounts as follows. Current Base Unit Units for ery Small mounts Units for ery Large mounts Symbol μ m k M Pronounced s mpere Microampere Milliampere Kiloampere Megampere (mp) Multiplier 1 0.000001 0.001 1,000 1,000,000 28 Section 1 Fundamentals of Electricity

mmeter OFF OFF COM Figure 4-5 Figure 4-3 oltage (, EMF, or E) is electric pressure, a potential force or difference in electric charge between two points. oltage pushes current through a wire similar to water pressure pushing water through a pipe. The voltage level or value is proportional to the difference in the electric potential energy between two points (Figure 4-4). oltage is measured in volts (). voltage of 1 volt is required to force 1 ampere of current through 1 ohm of resistance. The letter E, which stands for emf (electromotive force), or the letter, which stands for voltage, is commonly used to represent voltage in an algebraic formula. oltage, or a difference in potential, exists between any two charges that are not exactly equal to each other. Even an uncharged body has a potential difference with respect to a charged body; it is positive with respect to a negative 1 olt difference between charges charge and negative with respect to a positive charge. oltage also exists between two unequal positive charges or between two unequal negative charges. Therefore, voltage is purely relative and is not used to express the actual amount of charge, but rather to compare one charge to another and indicate the electromotive force between the two charges being compared. voltmeter is used to measure the voltage, or potential energy difference of a load or source, as illustrated in Figure 4-5. oltage exists between two points and does not flow through a circuit as current does. It is possible to have voltage without current, but current cannot flow without voltage. voltmeter is connected across, or in parallel, with the two points. ery small amounts of voltage are measured in milli1 1 and microvolts, whereas high-voltvolts 1,000 1,000,000 age values are expressed in kilovolts (1,000) and megavolts (1,000,000). The typical units of measurement are as follows. ( ) ( ) 1 Ohm resistance 1 mp current oltage is proportional to the difference between charges. oltage Base Unit Symbol Units for ery Small mounts Units for ery Large mounts μ m k M Pronounced s olt Microvolt Millivolt Kilovolt Megavolt Multiplier 0.000001 0.001 1,000 1,000,000 Chapter 4 pet34317_ch04_027-034.indd 29 oltmeter connected to measure voltage. mmeter connected to measure current. 4.2 oltage Figure 4-4 COM 1 Electrical Quantities and Ohm s Law 29 22/11/12 3:48 PM

4.3 Resistance Resistance (R) is the opposition to the flow of electrons or current. Basically, resistance is the measure of electric friction as electrons move through a conductor. Resistance is measured in ohms. The Greek letter (omega) is used to represent ohms, and the typical units of measurement are as follows. example, a multimeter contains an ohmmeter that operates by a battery located inside the instrument. The ohmmeter applies a known voltage into a circuit, measures the resulting current, and then calculates the resistance. For this reason ohmmeters should never be connected to live circuits! PRT 1 Review Questions 1. What is the practical unit of electric charge? Resistance Base Unit Symbol Ω Units for ery Small mounts Units for ery Large mounts μω mω Pronounced s Ohm Microhm Milliohm Kilohm Megohm Multiplier 0.000001 0.001 1,000,000 1 kω 1,000 MΩ Resistance is due, in part, to each atom resisting the removal of an electron by its attraction to the positive nucleus. Collisions of countless electrons and atoms as the electrons move through the conductor create additional resistance. The resistance created causes heat in the conductor when current flows through it; that is why a wire becomes warm when current flows through it. The higher the resistance of a conductor, the greater its opposition to current flow. The elements of an electric range become hot and the filament of an incandescent lamp becomes extremely hot because they have a much higher resistance than the conductors that carry the current to them. Every electric component has resistance, and this resistance changes electric energy into another form of energy such as heat, light, or motion. n ohmmeter is used to measure resistance, as illustrated in Figure 4-6. Unlike the voltmeter and ammeter, which use energy in the current to make their measurements, the ohmmeter uses its own power source. For 2. Define electric current. 3. What is the basic unit used to measure current? 4. Explain what a current flow of 1 ampere can be equated to. 5. ccount for the fact that electric current travels at the speed of light, while the electron movement is relatively slow. 6. How must an ammeter be connected into a circuit to measure current? 7. Define voltage. 8. What is the basic unit used to measure voltage? 9. Explain what a voltage of 1 volt can be equated to. 10. How must a voltmeter be connected into a circuit to measure voltage? 11. Define electric resistance. 12. What is the basic unit used to measure resistance? 13. What is the cause and effect of resistance? 14. When using an ohmmeter to measure resistance, what precaution must be observed? 15. Convert the following data: a. 12,000 to k b. 0.04 to m c. 1.8 MΩ to Ω d. 40 μ to Part 2 Power, Energy, and Ohm s Law OFF Figure 4-6 30 COM Ohmmeter connected to measure resistance. 4.4 Power Electric power (P) is the amount of electric energy converted to another form of energy in a given length of time. Power represents the work performed by an electric circuit and is measured in watts (W). Power in an electric circuit is equal to Power = voltage current Watts = volts amperes P = EI Section 1 Fundamentals of Electricity pet34317_ch04_027-034.indd 30 22/11/12 3:48 PM

Wattmeter 1440 W 120 12 Figure 4-7 I 100 W ppliance power rating. Figure 4-8 Wattmeter connected to measure power. where P = the power in watts E = the voltage in volts I = the current in amperes The electric power rating of an appliance is listed on its nameplate as illustrated in (Figure 4-7). This rating is not always specified simply in terms of watts. Power rating may be given in voltage and current, in which case, the power can be calculated using the equation P = EI. When the rating is given in watts and volts, the rated current can be calculated using the equation P I = E EXMPLE 4-1 Problem: n iron draws 10 from an 120- household supply. How much power is used? motion, they have kinetic energy, or the energy of motion. The unit of energy, called the joule (J), is used in scientific work to measure electric energy. By definition, a joule is the amount of energy carried by 1 coulomb of charge propelled by an electromotive force of 1 volt. The watt-hour (Wh) is the more practical unit of measurement of electric energy. Power and time are factors that must be considered in determining the amount of energy used. This is usually done by multiplying watts by hours. The result is watt-hours. If power is measured in kilowatts and multiplied by hours, the result is kilowatthours, abbreviated kwh. Energy measurements are used in calculating the cost of electric energy. kilowatthour meter connected to a residential electrical system is used to monitor your daily power usage as illustrated in Figure 4-9. P = EI = 120 10 = 1,200 W, or 1.2 kw Power can be measured using a wattmeter. The wattmeter is basically a voltmeter and ammeter combined into one instrument (Figure 4-8). The ammeter terminals are connected in series, and the voltmeter terminals are connected in parallel with the circuit in which the power is being measured. The wattage rating of a lamp indicates the rate at which the device can convert electric energy into light. The faster a lamp converts electric energy to light, the brighter the lamp will be. 4.5 Energy Electric energy refers to the energy of moving electrons. In an operating electric circuit, the voltage pushes and pulls electrons into motion. When electrons are forced into Figure 4-9 Chapter 4 pet34317_ch04_027-034.indd 31 Kilowatt-hour meter. Electrical Quantities and Ohm s Law 31 22/11/12 3:48 PM

EXMPLE 4-2 Problem: ssuming that the cost of electricity is 5 cents ($0.05) per kwh, how much will it cost to operate a 100-W lamp continuously for 200 hours? kwh = 100 W 200 h 1,000 = 20 kwh Cost = kwh rate = 20 $0.05 = $1.00 Power source (battery) Protective device (fuse) Control device (switch) Conductor (wire) Figure 4-11 Electric circuit schematic diagram. Load device (lamp) 4.6 Electric Circuit The essential parts of an electric circuit consist of a power source, protection device, conductors, control device, and load. closed circuit is a closed loop or path from one side of a voltage source to the other, as illustrated in Figure 4-10. complete or closed circuit is needed for current to flow. If the circuit is broken at any point, there is no longer a closed loop and no current can flow. This is often referred to as an open circuit. Control device Electron current flow Load device Figure 4-11 shows the schematic diagram for an electric circuit. pictorial circuit diagram uses simple images of components, while a schematic diagram shows the components of the circuit as simplified standard symbols; both types show the connections between the devices. The function of the parts can be summarized as follows: Battery power source supplies the electric pressure or voltage required to push current through the circuit. Conductors provide a low-resistance path from the source to the load. Switch control device opens and closes the circuit to switch the current flow OFF and ON. Lamp load converts the electric energy from the power source into light and heat energy. Fuse protection device melts to automatically open the circuit in the event of a higher than rated current flow. Too much current can cause damage to conductors and load devices. Power source Figure 4-10 Closed electric circuit. Protection device 4.7 Ohm s Law Ohm s law defines the relationship between circuit current, voltage, and resistance and is stated as follows: The current flowing in a circuit is directly proportional to the applied voltage and inversely proportional to the resistance. Rated voltage 12 olts Lower voltage 6 olts Higher voltage 18 olts 4 2 6 3 3 3 Figure 4-12 Effect of voltage on current flow. 32 Section 1 Fundamentals of Electricity

12 olts 12 olts 12 olts 4 12 1 Therefore, the higher the voltage applied to a circuit, the higher the current through the circuit. On the other hand, a decrease in the applied voltage will result in a decrease in circuit current. This assumes that the circuit resistance remains constant, as illustrated in Figure 4-12. If the voltage is held constant, the current will change as the resistance changes, but in the opposite direction. ssuming that voltage is constant, lowering the resistance causes an increase in current. On the other hand, an increase in resistance results in a decrease in current flow, as illustrated in Figure 4-13. Ohm s law can be stated as mathematical equations, all derived from the same principle as follows: I = R E (current = voltage divided by resistance) E = I R (voltage = current multiplied by resistance) R = E I (resistance = voltage divided by current) EXMPLE 4-3 Problem: portable heater with a resistance of 10 Ω is plugged into a 120-volt electrical outlet. How much current will flow to the heater? 3 1 12 Initial resistance Lower resistance Higher resistance Figure 4-13 Effect of resistance on current flow. I = R E = 120 10 Ω = 12 EXMPLE 4-4 Problem: If a 25-Ω resistor has a current flow of 2 through it, how much is the voltage across it? EXMPLE 4-5 E = IR = 2 25 Ω = 50 Problem: What is the resistance of a toaster element that is rated for 120 and 8? R = E I = 120 8 = 15 Ω 4.8 Direction of Current Flow The direction of current flow in a circuit can be designated either as electron flow or conventional current flow, as illustrated in Figure 4-14. Electron flow is based on the electron theory of matter and follows the motion of electrons in the circuit from negative to positive. Conventional current Electron flow (negative to positive) Figure 4-14 Electron versus conventional current flow. Conventional flow (positive to negative) Chapter 4 Electrical Quantities and Ohm s Law 33

flow is based on an older theory of electricity and assumes a current flow in the opposite direction from positive to negative. Both conventional current flow and electron flow are acceptable and are used for different applications. For purposes of circuit analysis it makes no difference which direction of current flow you use as long as the same direction is used consistently throughout the circuit. It is important to understand and be able to think in terms of both conventional current flow and in terms of electron flow. PRT 2 Review Questions 1. D efi ne electric power. 2. What is the basic unit used to measure electric power? 3. toaster draws 8 amperes when connected to a 120-volt source. What is the wattage rating of the toaster? 4. Explain why a 140-W soldering iron produces more heat than a 20-W soldering iron. 5. D efi ne electric energy. 6. What is the basic unit used to measure electric energy? 7. Is it more expensive to operate a 1,000-W hair dryer for 5 minutes or a 40-W lamp for 1 hour? Why? 8. Compare a closed and an open electric circuit. 9. State the function of each of the following components of a circuit: a. Power sou rc e b. Conductor s c. Cont r ol d ev ic e d. P r ot e ct ion d ev ic e e. L oa d 10. What does Ohm s law tell us about current flow in a circuit? 11. Ohm s law is applied to a circuit using what three mathematical equations? 12. load has a resistance of 20 Ω. What is its current when connected to 240? 13. How much resistance does a load have if it draws a current of 6 from a 12- battery? 14. 12 - Ω load is conducting a current of 2.5 amps. How much is its voltage? 15. Compare the direction of electron flow and conventional current flow. 34 Section 1 Fundamentals of Electricity