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} | | 1 | | | | i | | l | l f r M ) ~ - pr A ‘\; - N | m p i n Name_ (UM A HTING Date ! 0| LL Partners {)\k}‘“ N, 70N \ LaB 7: KIRCHHOFF's cIRculT RULES The Energizer© keeps on going, and going, and . . . . —Eveready Battery Company, Inc. OBJECTIVES e To learn how multimeters are designed so that they don’t modify the currents and voltages being measured. e To learn to measure resistance with a multimeter. ¢ To develop a method for calculating the equivalent resistance of resistors con- nected in series. e To develop a method for calculating the equivalent resistance of resistors con- nected in parallel. e To understand Kirchhoff’s circuit rules and use them to determine the cur- rents that flow in various parts of DC circuits. OVERVIEW In the last few labs, you have examined simple circuits with bulbs or resistors connected in series and parallel. The emphasis has been on learning about the concepts of current, voltage, and resistance in fairly simple DC circuits. In this lab you will look at circuits more quantitatively. Up until now you have been using computer-based sensors to measure currents and voltages. A mul- timeter is a device with the capability of measuring current and voltage. Some multimeters can also be used to measure resistance. In Investigation 1, you will learn how to use a multimeter to measure current, voltage, and resistance. LAB 7: KIRCHHOFF'S CIRCUIT RULES 129

130 In Investigation 2, you will look at circuits with resistors connected in both series and parallel and discover the rules for finding the equivalent values of net- works of resistors wired in series and parallel. Sometimes circuit elements are connected with multiple b complicated ways than simply in series or parallel. The rules for series and par- allel addition of resistances are not adequate to determine the currents flowing in such circuits. In Investigation 3 of this lab, you will learn about Kirchhoff’s circuit rules that are generally applicable to all types of circuits. atteries in more INVESTIGATION 1: MEASURING CURRENT, VOLTAGE, AND RESISTANCE Resistance, voltage, and current are fundamental electrical quantities that char- acterize all electric circuits. The multimeters available to you can be used to measure these quantities. All you need to do is choose the correct dial setting, connect the wire leads to the correct terminals on the meter, and connect the meter correctly in the circuit. Figure 7-1 shows a simplified diagram of a multimeter. (e ) Scales: 3 ~ L! K=10% 'l m=1073 M = 10° Direct current volts — DCV__ACV DCV : — Dial for selection of measurement type and scale Ohms —Q R DCA +— Direct current amps VQ CO MA 10A (o) o] & @j— Receptacles for input leads (a) (b) Figure 7-1: (a) Multimeter with voltage, current, and resistan"ce modes, and (b) symbols that will be used to represent a multimeter when it is used as an ammeter, voltmeter, or ohmmeter, respectively. A current sensor and a multimeter used to measure current are both connected in a circuit in the same way. Likewise, a voltage sensor and a multimeter used to measure voltage are both connected in a circuit in the same way. The next two activities will remind you how to connect them. The activities will also show you that when meters are connected correctly, they don’t change the currents or volt- ages being measured. You will need: ¢ digital multimeter o 2 very fresh, akaline 1.5-V D cell batteries with holders e 6 alligator clip leads e 2 #14 bulbs and sockets REALTIME PHYSICS: ELECTRICITY AND MAGNETISM e

Activity 1-1: Measuring Current with a Multimeter ~ Figure 7-2 shows two possible ways that you might connect a multimeter to mea- sure the current flowing through bulb 1. Prediction 1-1: Which of the diagrams in Figure 7-2, (b) or (c), shows the cor- rect way to connect a multimeter to measure the current through bulb 1? Explain why it should be connected this way. [Hint: In which case is the current flowing through the multimeter the same as that flowing through bulb 17] d \O\O ;( O \filn\ C 1 @ O ’@‘ 1 z ©: ©: d (a) (b) (e Figure 7-2: (a) A circuit with two light bulbs and a battery, and two possible but not necessar- ily desirable ways to connect a multimeter to measure current: (b) in series with bulb 1, and () in parallel with bulb 1. 1. Set up the basic circuit in Figure 7-2a. Use two batteries in series to make a 3-V battery. Observe the brightness of the bulbs. 2. Set the multimeter to measure current and connect it as shown in Figure 7-2b. Was the brightness of the bulbs significantly affected? [\() 3. Now connect the meter as in Figure 7-2c. Was the brightness of the bulbs sig- nificantly affected? %65 b\)lp A do@sn{ ltgh‘\’ ve Question 1-1: If the multimeter is connected correctly to measure current, it should measure the current flowing through bulb 1 without significantly affect- ing the current flowing through the bulb. Which circuit in Figure 7-2 shows the correct way to connect a multimeter? Explain based on your observations. Why is it connected in this way? B, becaue the Dulps weront afected Question 1-2: Does the multimeter appear to behave as if it is a large resistor or a small resistor? Explain based on your observations. Why is it designed in this way? small resistor pecavse wnen vsed Correct K AoRs NOr okect ‘he Coneny wirhin The CI( | Activity 1-2: Measuring Voltage with a Multimeter Figure 7-3 shows two possible ways that you might connect a multimeter to mea- sure the potential difference across bulb 1. 131 LAB 7: KIRCHHOFF'S CIRCUIT RULES

132 Prediction 1-2: Which of the diagrams in Figure 7-3 shows the correct way to connect a multimeter to measure the voltage across bulb 1? Explain why it should be connected this way. ) (a) (b) Figure 7-3: Two possible but not necessarily desirable ways to connect a multimeter to measure voltage: (a) in series with bulb 1, and (b) in parallel with bulb 1. 1. Set the meter to measure voltage and connect it as in Figure 7-3a. Was the brightness of the bulbs significantly affected? ho 2. Now connect the meter as in Figure 7-3b. Was the brightness significantly affected? nD Question 1-3: If the multimeter is connected correctly, it should measure the volt- age across bulb 1 without significantly affecting the current flowing through the bulb. Which circuit in Figure 7-3 shows the correct way to connect the multimeter? Explain based on your observations. Why is it connected in this way? [Hint: In which case is the voltage across the multimeter the same as that across bulb 1?] SO 1 can CO(TCC‘\'\L& measvre, the voviage Question 1-4: Does the multimeter behave as if it is a large resistor or a small resistor? Explain based on your observations. Why is it designed in this way? SHAl (eSiSrar e COVSe |+ dloesn Offect the curreny /voage hivigin clcour You just observed that even multimeters have some resistance. Now you will investigate how to measure resistance with a multimeter. In earlier labs, you observed that the resistance of a light bulb increases when the current through it causes the temperature of the filament to rise. To make the behavior of circuits more consistent, it is desirable to have circuit elements with resistances that do not change. For that reason, circuit elements known as resis- tors have been invented. The resistance of a well-designed resistor doesn’t vary with the amount of current passing through it (or with temperature), and resis- tors are inexpensive to manufacture. The most common resistors contain a form of carbon known as ).’,I'.\}‘]\il\‘ Sus- pended in a hard glue binder. It is usually surrounded by a plastic case with a color code painted on it Figure 7-4 depicts a carbon resistor cut down the middle REALTIME PHYSICS: ELECTRICITY AND MAGNETISM

Cross section of graphite material. Figure 7-4: A cutaway view of a carbon resistor. Figure 7-5 shows a carbon resistor with colored bands that tell you the value of the resistance and the tolerance (guaranteed accuracy) of this value. Figure 7-5: A carbon resistor with color bands. The first two stripes indicate the two digits of the resistance value. The third stripe indicates the power of ten multiplier, and the fourth stripe signifies the resistor’s tolerance. The key in Table 7-1 shows the corresponding values. Table 7-1: The resistor code Bands A, B, C violet = 7 black = 0 gray = 8 brown = 1 white = 9 red = 2 orange = 3 Band D yellow = 4 none = =20% green = 5 silver = *£10% blue = 6 gold = *5% As an example, look at the resistor in Figure 7-6. Its two digits are 1 and 2 and the multiplier is 10%, so its value is 12 X 102, or 12,000 ). The tolerance is +20%, so the value might actually be as large as 14,400 Q or as small as 9600 (1. Brown Orange Figure 7-6: An example of a color-coded carbon resistor. The resistance of this resistor is 12 %X 10% 0 = 20%. The appropriate way to connect -the multimeter to measure resistance is shown in Figure 7-7. When the multimeter is in its ohmmeter mode, it connects a known voltage across the resistor and measures the current through the resistor. Then resistance is calculated by the meter from R V/I. LAB 7: KIRCHHOFF'S CIRCUIT RULES

134 Note: Resistors must be isolated (disconnected from the circuit) before their resistances can be measured. This also prevents damage to the multimeter that may occur if a voltage is connected across its terminals while in the resistance mode. R Figure 7-7: Connec- tion of an ohm- meter to measure resistance. In the next activity, you will use the multimeter to measure the resistance of sev- eral resistors. You will need e several color-coded resistors e 2 digital multimeters ® 6-V battery Activity 1-3: Reading Resistor Codes and Measuring Resistance 1. Choose several resistors and read their codes. Record the resistances and the tolerances in the first two columns of Table 7-2. Table 7-2 R from Tolerance Measured Measured Measured R = V/I code (1)) from code R () V (V) 1 (A) Q) 23_N| +5% [22.8-1[3.L\V |00l A |92.40 5.0 | 25 [14 1303V 0.4ga [1S.00 290 |25 390 [3.w2V 0.093p (2890 ol | £51 Q@20 |3.02V |D03TA |971.80 There are two ways to determine resistance with the multimeter. One is to use the resistance mode and measure the resistance directly. The second is to connect the resistor to a battery and then measure the voltage across the resistor and the current through the resistor. R can then be calculated from Ohm’s law, R = V/I. You will use both of these methods to measure the resistances of the resistors you selected. 2. Measure the resistance of each of your resistors directly using the multimeter and enter the values in Table 7-2 under “Measured R.” 3. Be sure to reset the multimeter to measure current and voltage, respectively, or you will burn out the fuse in the meter. Connect each resistor to the battery and simultaneously measure the voltage across the resistor and the current through the resistor with the multimeters. Record V and I in the appropriate columns of Table 7-2 and calculate the resistance from these values. REALTIME PHYSICS: ELECTRICITY AND MAGNETISM i—

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