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NIDA SERIES 130E Block 3 BASIC DC CIRCUITS BASIC ELECTRICITY UNIT I - DC CIRCUITS LESSON 1 OHM'S LAW AND POWER OBJECTIVES OVERVIEW On completion of this lesson, the student will be able to: This lesson is the first one in which students study electrical circuit behavior. 1. State Ohm's Law and define the relationship between current, voltage, and resistance. Ohm's Law is discussed, and the relationship of current, voltage, and resistance is analyzed. 2. Solve problems for unknown quantities of current, voltage, and resistance using Ohm's Law. The three formulas that express the relationship of current, voltage, and resistance are presented. 3. Draw and use the circular expression of Ohm's Law to help learn the Ohm's Law formulas. Students learn to use these three formulas by solving problems for unknown values of current, voltage, and resistance. 4. Define power in an electrical circuit in terms of current and voltage. 5. Demonstrate the ability to use Ohm's Law with circuit measurements. PREREQUISITES None EQUIPMENT REQUIRED Nida Model 130E Test Console Nida Series 130 Experiment Card PC130-5 Nida Model 480/488 Multimeter, or equivalent Copyright © 2002 by Nida Corporation Students learn to draw the circular expression of Ohm's Law. They learn to use this circle as a tool to help them learn and remember the three Ohm's Law formulas. The relationship of power to current and voltage is explained. The power formula that expresses this relationship is presented. Students learn to use the power formula to calculate the power in a circuit. In the experiment, students measure current, voltage, and resistance; and solve problems to demonstrate their understanding of Ohm's Law. 3-1-1 LESSON 1 OHM'S LAW AND POWER UNIT I Block 3 Basic DC Circuits INTRODUCTION The late 1700s and early 1800s saw a rapid growth in the development of new electrical devices. One of these devices was the first battery made in 1796 by an Italian named Volta. A significant development came in 1827 by a German named George Simon Ohm, who developed the relationship of current, voltage, and resistance in an electrical circuit. Ohm announced this relationship in what became known as Ohm's Law. Ohm's Law is perhaps the most important law in the study of electrical circuits, since the relationship defined in the law is basic to all circuit operation. Memorize and learn how to use Ohm's Law so that you build a strong foundation for your study of electronics. VOLTAGE, CURRENT, AND RESISTANCE Ohm's Law states the relationship of three electrical quantities: voltage, current, and resistance. What are these three quantities? What do they do? How do we identify them? These questions are answered in Table 1, which lists the three quantities, their units of measure, the symbols that identify them, and the function of each quantity in an electrical circuit. Table 1. Voltage, Current, and Resistance QUANTITY Name UNIT OF MEASURE Symbol Name Symbol DEFINITION Voltage E Volt V Voltage is the electrical pressure or force which makes current flow in a circuit. Current I Ampere A Current is the flow of electrons through a circuit. Resistance R Ohm Ω Resistance is the opposition to current flow offered by electrical devices in a circuit. Ohm's Law states: OHM'S LAW THE CURRENT (I) IN AN ELECTRICAL CIRCUIT IS DIRECTLY PROPORTIONAL TO THE VOLTAGE (E) AND INVERSELY PROPORTIONAL TO THE RESISTANCE (R). 3-1-2 Copyright © 2002 by Nida Corporation Block 3 Basic DC Circuits UNIT I LESSON 1 OHM'S LAW AND POWER The Ohm's Law relationship of current, voltage, and resistance is expressed in three formulas: I= E R R= Current equals voltage divided by resistance. E I E= IR Resistance equals voltage divided by current. Voltage equals current times resistance. In other words, what Ohm's Law means is that the current in an electrical circuit depends on two things: The voltage applied to the circuit The resistance in the circuit This relationship of current, voltage, and resistance in a circuit can be more easily understood if you compare the circuits in Figure 1 and Figure 2. The circuits in Figure 1 have a fixed resistance. Note that when the voltage increases, the current also increases; when the voltage decreases, the current also decreases. The current, therefore is directly proportional to the voltage. If you increase the voltage in a circuit with a fixed resistance, the current increases. 1A. Current Increases If you decrease the voltage in a circuit with a fixed resistance, the current decreases. 1B. Current Decreases Figure 1. Current is Directly Proportional To Voltage Copyright © 2002 by Nida Corporation 3-1-3 LESSON 1 OHM'S LAW AND POWER UNIT I Block 3 Basic DC Circuits Now look at Figure 2. The circuits in Figure 2 have a fixed voltage. Note that when the resistance increases, the current decreases; when the resistance decreases, the current increases. Thus, the current is inversely proportional to the resistance. If you increase the resistance in a circuit with a fixed voltage, the current decreases. 2A. Current Decreases If you decrease the resistance in a circuit with a fixed voltage, the current increases. 2B. Current Increases Figure 2. Current is Inversely Proportional to Resistance Example: Ohm's Law and Voltage, Current, and Resistance. Look at the electrical circuit in Figure 3. The voltage source (E), a battery, is connected to a resistive load (R) through a current meter which will measure the current (I) of the circuit. How much current (I) flows in the circuit if voltage (E) is 1 volt and resistance (R) is 1 ohm? Figure 3. Electrical Circuit Using Ohm's Law, you know the formula for I: I= E R Insert the values for voltage and resistance into the formula, and solve for current: I= 1V =1 A 1Ω The answer is that a voltage of 1 volt across a resistor of 1 ohm causes a current flow of 1 ampere. 3-1-4 Copyright © 2002 by Nida Corporation Block 3 Basic DC Circuits UNIT I LESSON 1 OHM'S LAW AND POWER What happens now, if you increase the voltage (E) to 12 volts but the resistance (R) remains at 1 ohm? Does current increase or decrease? Using Ohm's Law, you find that: I= E R = 12 V 1Ω = 12 A When voltage increases and resistance remains the same, current increases proportionately to voltage. Try one more. What happens if the voltage (E) remains at 12 volts, but the resistance (R) increases to 24 ohms? Does current increase or decrease? Again you use Ohm's Law: I= E R = 12 V 24 Ω = 1V 2Ω = 0.5 A = 500 mA As you can see, the current decreased. Exercise 1: Solve for an Unknown Quantity, Given Two Known Quantities. Table 2 contains ten problems. Problem 1 has already been completed as an example. Enter the your answers for the remaining problems in the appropriate blanks in the table. Answers must include the basic unit of measure (V, A, or Ω). Enter the formulas you use and your calculations in the appropriate columns. Use the circuit diagram of Figure 3, if necessary, to help you visualize the circuit. Table 2. Solve for the Unknown Quantities NO. 1 VOLTAGE CURRENT RESISTANCE 12.0 V 3.0 A 4Ω 0.5 A 48 Ω 2 3 9.0 V 4 5 6.0 V 6 9.0 V 7 12.0 V 8 10.0 V 10 4.5 V E R E = IR CALCULATION 12 =3A 4 .5 x 48 = 24 V E I 1000 Ω 600 Ω 30.0 mA 1.2 kΩ 15.0 mA 9 I= R= 3.0 A 0.045 A FORMULA 1.0 kΩ aA Copyright © 2002 by Nida Corporation 18.0 kΩ 3-1-5 LESSON 1 OHM'S LAW AND POWER UNIT I Block 3 Basic DC Circuits CIRCULAR EXPRESSION OF OHM'S LAW The circular expression of Ohm's Law is a simple tool to aid you in learning and using Ohm's Law. Figures 4A, 4B, 4C, and 4D illustrate the circle and how to use it. The circle is divided into 3 sections, as you can see below: E is in the top section; I and R are in the bottom 2 sections. Put your finger over I to solve for current. You see two letters left: E over R, or E divided by R. I= 4A. The Circle E R Put your finger over R to solve for resistance. You see two letters left: E over I, or E divided by I. R= 4B. Current E I Put your finger over E to solve for voltage. You see two letters left: I beside R, or I times R. E = IR 4C. Resistance 4D. Voltage Figure 4. Circular Expression of Ohm's Law POWER Now that you understand the relationship of current, voltage, and resistance in electrical circuits, you can learn about another important electrical quantity: power. What is power? What does power do? How does power relate to current and voltage? These questions are answered in Table 3. Table 3. Power QUANTITY UNIT OF MEASURE Name Symbol Name Symbol Power P Watt W DEFINITION Power is the amount of work performed by a circuit when the voltage forces current to flow through the resistance. In other words, power is the amount of work performed by an electrical circuit, and the amount of work depends on how much voltage is required to force the current to flow through the resistance. Thus, power is directly proportional to voltage and current. 3-1-6 Copyright © 2002 by Nida Corporation Block 3 Basic DC Circuits UNIT I LESSON 1 OHM'S LAW AND POWER Work performed by electrical circuits is in the form of heat which is generated when voltage forces current to flow through resistance. This work can be either useful work or nonuseful work. Nonuseful work is heat produced by the resistors which adjust or control the amount of current that flows in electrical circuits. The heat is not used and is simply an undesirable byproduct of the resistors' function of controlling current. This use of power by resistors to produce nonuseful heat is called power dissipation because the power is dissipated, or given off, by the resistors. With useful work, on the other hand, the purpose of the resistors in electrical circuits is to generate heat rather than to control the current. In this case, the fact that resistors control the current is a byproduct of their function of generating heat. Useful work is heat produced by an electrical circuit to do such things as illuminate a light bulb to light up a room or heat a toaster to toast bread. You use electricity because you want it to do work for you, such as produce light. Take a flashlight, for example. The electrical circuit of a flashlight consists of a battery to generate the voltage which forces the current (controlled by a switch) to flow through a resistor (a light bulb). This circuit is illustrated in Figure 5. R is a light bulb. E is a battery. S is an ON/OFF switch. Figure 5. Electrical Circuit of Flashlight The work performed by the flashlight circuit results in the light produced by the light bulb. The amount of light produced by the flashlight depends on how much voltage the battery produces to force the current through the resistance of the light bulb. Thus, power (the amount of work an electrical circuit performs) depends on how much voltage is needed to force the current to flow through the resistance in the circuit. As was stated before, power is directly proportional to voltage and current. This relationship of power, voltage, and current can be stated in two ways: 1. One watt of power is used when 1 volt causes 1 ampere to flow through a circuit. 2. Power equals voltage times current: P = EI. Copyright © 2002 by Nida Corporation 3-1-7 LESSON 1 OHM'S LAW AND POWER Example: UNIT I Block 3 Basic DC Circuits Solve for Power in an Electrical Circuit Using P = EI. Assume that the voltage source for the flashlight in Figure 5 is two 1.5 V batteries, and the resistance of the light bulb is 6 Ω. You know the voltage of the 2 batteries: E = 2 batteries x 1.5 V each = 3 V You know the resistance of the light bulb: R=6Ω You do not know the current, so use Ohm's Law to solve for current: I= Insert the values for E and I into the formula for power: P = EI = 3 V x 0.5 A E 3V = = 0.5 A R 6Ω = 1.5 W The flashlight uses 1.5 W of power. This same problem can be solved in another, more direct way by using what is called the substitution method. Example: Solve for Power in an Electrical Circuit using P = EI and the Substitution Method. You do not know the current, but you do know voltage and resistance. You know the formula I= E solves for current, using Ohm's Law. R Insert this formula for I into the power formula for the unknown I: P = EI and I = Now insert the known values for E and R into the power formula: P = 3V× 3V 6Ω E R so: P = E × = 9 W 6 E R = 1.5 W The flashlight uses 1.5 W of power. The power formula can be expressed in several ways, depending upon how you prefer to write your formulas mathematically and upon what unknown quantity you have. The example above shows the substitution of the Ohm's Law formula which solves for current when current is unknown. When voltage is unknown, you substitute the Ohm's Law formula which solves for voltage: E = IR. Only some of the several ways for writing the power formula are given below. When you solve for power, use whichever ones work best for you. If current is unknown: P = E (E ÷ R) P = E× P= 3-1-8 E2 R E R If voltage is unknown: P = I(IR) P = I x IR P = I2R Copyright © 2002 by Nida Corporation Block 3 Basic DC Circuits UNIT I LESSON 1 OHM'S LAW AND POWER If you wish, you can memorize all these formulas. Memorizing them is not necessary, however, if you just remember that P = EI and E = IR. You can derive any formula you need from those two formulas. Exercise 2: Solve for Power, Given Two Known Quantities. Here are a few problems to give you practice solving for power. Show the formulas and your calculations for all problems. Use the circuit diagram in Figure 6, if needed, to help you visualize the circuit. Figure 6. Electrical Circuit GIVEN 1. E = 12 V R=6Ω CALCULATIONS P = EI = E× E R = 12 V × 12 V 6Ω = 24 W 2. I = 1.2 A E = 1.5 V 3. I = 100 mA E = 6 kV 4. E = 15 V R = 100 Ω 5. R = 1 kΩ I = 20 mA 6. I = 1.5 mA E = 24.0 V Copyright © 2002 by Nida Corporation 3-1-9 LESSON 1 OHM'S LAW AND POWER UNIT I Block 3 Basic DC Circuits 20. Calculate the percent of error for your current values in Table 4. Record your answers in Table 4 (% ERROR). Your calculations should show you that Ohm's Law and the relationship of current, voltage, and resistance is valid, since the percent difference between your measured values and your calculated values is within the expected limits of error. 21. Calculate the power that is dissipated in each of the three resistors on PC130-5 at all the voltages applied, as shown in Table 4. Use your measured current values for your calculations. Record your answers in Table 4 (POWER). SUMMARY In this lesson on Ohm's Law, you should have learned the following: Current in electrical circuits is directly proportional to the voltage in the circuit. Current in electrical circuits is inversely proportional to the resistance in the circuit. Ohm's Law is one of the most significant laws in electronics, since the relationship defined in the law is basic to all circuit operation. The Ohm's Law relationship of current, voltage, and resistance in an electrical circuit is expressed in the following formulas. I= E R E = IR R= E I The circular expression of Ohm's Law is a tool you can use to help you remember these three formulas. Power is the term which describes the amount of work an electrical circuit can do. Power is directly proportional to current and voltage. The power relationship of current and voltage is expressed in the following formulas. P = EI 3-1-14 P= E2 R P = I2R Copyright © 2002 by Nida Corporation