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1 RESISTANCE & OHM S LAW (PART I and II) - 8 Objectives: To understand the relationship between applied voltage and current in a resistor and to verify Ohm s Law. To understand the relationship between applied voltage and current in a Light Emitting Diode (LED). To understand simple parallel and series circuits and to use this understanding to determine the circuit connections of a hidden black box resistor network. To test the connection between resistance, current, voltage, and power dissipation. Equipment: Digital multi-meters(2 per group)(dmm for short), variable power supply (prefer 0-18 Volt), snap-on-circuit-board, 6V lamps, resistors, LED's of different colors. A multi-meter is a device that can be used as a voltmeter, an ammeter, or an ohmmeter. Background: Electric resistance, R, is defined by: R = V / I, (1) where V is the potential difference (or voltage drop) across the resistor and I is the current through it. The unit of resistance is the Ohm. ( = Volt/Ampere = V/A). If R = 0 in a circuit, it is called a "shorted" circuit; if R =, it is called an open circuit. The product P = I V is the power dissipated in the resistor (of course P = I V = I 2 R = V 2 / R ). Ohm's Law: For many materials resistance R is a constant, independent of I and V. The linear relationship between V and I, V = I R is called Ohm s Law. Materials obeying Ohm s Law are said to be "Ohmic" materials. (Simple light bulbs do NOT satisfy this Law, manufactured resistors do. An LED does NOT obey Ohm s Law. ) Equivalent Resistance: When several resistors are connected together, they can also be replaced with a single resistor that will have the same potential drop and draw the same total current as the combination of resistors. This resistance is called the equivalent resistance R eq of the circuit. Resistors in Series: Figure 1. Series Connections When the same current flows through each of a number of resistors, they are said to be in series. The equivalent resistance R eq for resistors connected in series is Ohm 1

2 R eq R i (2) i Note that here R eq is larger than any of the individual resistances. Resistors in Parallel Figure 2. Parallel Connections When the same potential difference appears across each of a number of resistors, they are said to be in parallel. The equivalent resistance R eq for resistors connected in parallel is 1 1 (3) Req R i i Note that here Req is smaller than any of the individual resistances. Electrical Measurements: A voltmeter is a device to measure the potential drop across a circuit or across part of a circuit. A voltmeter has a very large resistance so that the current through it is negligible, and it can be assumed that the potential drop across the resistor in Fig. 3a is the same whether or not the voltmeter is attached. A voltmeter is always connected in parallel with the circuit element whose potential difference is to be measured. An ammeter is a device to measure the current through a circuit element. It has a very small resistance so that the potential drop across is negligible, and it can be assumed that the current through the resistor in Fig. 3b is the same whether or not the ammeter is inserted in the circuit. An ammeter is always connected in series with circuit element whose current is to be measured. If you do not connect the ammeter the correct way, you can severely damage the device. Ohm 2

3 Figure 3a Voltmeter Connection Figure 3b Ammeter Connection An ohmmeter is a device that measures resistance. It is connected in parallel across the resistance to measured. You should NOT measure the resistance of a resistor that is still part of a circuit. You will probably destroy the ohm-meter, certainly you will measure the wrong resistance. In practice first disconnect all leads of the resistor to be measured, so no electric current runs through the resistor, except for the current supplied by the battery inside the ohm-meter itself. If you do not connect the Ohmmeter the right way, you can severely damage the device. PART I Diagnostic Phase: You should always make a schematic drawing on paper before building any circuit! Make a simple circuit on the snap-on-circuit-board, consisting of three 6V lamps in series and a variable power supply. Start at low power output and slowly turn up the power until the lamps start to glow. Switch the multi-meter to the Voltage Mode and measure the total voltage difference over the entire circuit, then the voltage drop over each lamp. Interupt the circuit and reconnect but insert also the leads of the multimeter, switch the multi-meter to the Ampere Mode. You now measure the electric current flowing out of the power supply, through the circuit and through each lamp. Since by now you have become an expert in electric circuits, put the lamps back in the box and let s start with the serious stuff. Activity 1: Ohms' Law. You will measure the resistance of an unknown resistor in three ways and verify that Ohm s Law applies: A. (Easy way): Use an ohmmeter to measure the resistance. See if the measured resistance remains the same if the leads to the ohmmeter are reversed. B. (Fancy but more realistic way): Connect an ammeter in series with the resistor and a voltmeter in parallel with it as shown below in figure 4, i.e. use two multi-meters in Ohm 3

4 the circuit. Use a variable output power supply to drive the circuit. As the output voltage is increased, measure I and V for a dozen values of V. To determine the resistance R and verify the linear relation of Ohm s Law, use Graphical Analysis and plot I versus V for a number of different voltage settings, make a linear fit to the data and obtain the correlation coefficient. From the slope you can obtain the resistance R. How? V A + Figure 4. Measuring voltage and current simultaneously of an Ohmic resistor. C. (Way for dummies): Read the commercial color coding of the resistor. Does it agree with A and B? Activity 2: Light emitting diode(led) - NON-Ohmic behavior. As an example of a device which does not obey Ohm's law, you will investigate an LED (Light Emitting Diode). For a NON-Ohmic device there is no easy way to measure its resistance with an ohmmeter. Actually its resistance is not fixed, but an I versus V plot clarifies its response to an applied voltage. A. Make a circuit by connecting a 100 ~ 200 ohm resistor in series with an LED. See figure 5. The resistor is put in to prevent burning out the LED. Connect a voltmeter across the resistor and measure the voltage across the resistor for several values of the supply voltage setting. (Keep the Voltage to be less than 5V and the current below 10 ma to prevent damage to the LED). Ohm 4

5 Since V power source = V ps is known, and V resistor + V LED = V ps, an alternative is to measure V LED directly. To measure the current I you can add an ammeter to the circuit as you did in Activity 1, or instead you can calculate each time the electric current I from the reading V resistor of the Voltmeter and the known value R of the resistor (V = I R for an Ohmic resistor). At what values of the current does the LED emit light, and at which values does it not emit light? Now reverse the leads from the power supply and repeat the measurement of current in the same range of voltage setting. Compare your observations with what you would expect for Ohmic behavior. B. Try another diode with a different color. ( Different materials have different electron energy gaps. As the electrons jump the gap this leads to emission of light of different colors. Available are LED s which emit red, green, yellow, or blue light.) v oltmeter resistor LED v oltage supply Figure 5. Measuring voltage and current for non-ohmic device. PART II Activity 3: Back to Ohmic resistors. For this activity you will use three resistors -- two with the same resistance and one with a different resistance (10 k 10 k and 20 k for example). A. Determine all possible ways you can connect the resistors in series and/or parallel to give different equivalent resistances. Draw a diagram of each of these combinations, and calculate the theoretical equivalent resistance. B. Set up two of the circuits in A on the breadboard and measure the actual equivalent resistance with a ohmmeter and compare with your calculation. C. Calculate the power dissipated by each resistor in the two circuits in B if a 12 V power supply is connected across the circuit. Ohm 5

6 Appendix: Resistors are coded with 4 colored stripes around the body of the resistor that allow easy determination of the resistance. The code for the first 3 colored bands is given below: RESISTOR COLOR CODES COLOR 1ST DIGIT 2ND DIGIT MULTIPLIER Silver Gold Black Brown Red Orange Yellow Green Blue Violet Gray White The 4-th colored band gives the "tolerance," i. e., the uncertainty in the marked resistance, as follows: gold: 5% silver: 10% no color: 20% Example: Figure 8. A Color Coded Resistor Helpful Hint: Most people who get incorrect results in this experiment do so because they fail to use the multi-meter correctly. Make sure the multi-meter is reading ohms AND that the gain or sensitivity is at the maximum number of significant digits for that resistance. Change the sensitivity by trial and error the maximum number of digits. Ohm 6

7 RESISTANCE & OHM S LAW (preliminary questions) Names: Section: You have three identical light bulbs each with a constant (assume Ohmic) resistance of 150. Suppose you connect the circuits to a 12 V battery. a.) Draw diagrams showing all the 4 possible ways they can be connected in series or parallel or in a combination of series and parallel. b.) You can identify brightness with Power (= Energy per second). How is the current I passing through each bulb related to the brightness? c.) Which of the circuits is the brightest, and which circuit is the dimmest? Ohm 7

8 Report -- RESISTANCE & OHM S LAW (Part I) Name: Section: Partners: Date: Part I Diagnostic Phase, building a circuit: On the snap-on-circuit-board construct a simple circuit of three 6V lightbulbs in series and connections to the variable power supply. Starting at low voltage, slowly turn up the voltage output of the power supply until the lamps start to glow. DO NOT GO HIGHER. Put the multi-meter on DC Volts (V=, not V~) and measure the total voltage over the three lamps. [WITHIN THE DC-VOLT RANGES ON THE MULTI-METER ALWAYS START WITH THE HIGHEST RANGE. If the reading is too low, turn to a lower range.] Now measure the voltage drop over each lamp. Put the multi-meter on DC Ampere [again start at highest range] and measure the electric current that flows out of the power supply. (In order to do this step, you have to interrupt the circuit and insert the leads of the Amp-meter). If you do not follow this step carefully, you may damage the multi-meter. Measure the current in between lamp 1 and lamp 2. Make a schematic drawing of the circuit, showing lamps, power supply and connecting wires. Mark the values of your measured voltages and currents in the circuit. Indicate direction of the current and + and for voltages. Ohm 8

9 Activity 1: Determine an unknown resistance in three ways (a, b, c) and verifying Ohm s Law. a.) Direct from Ohm-meter: reading = R unknown = Note that the resistor R unknown at this point should be free-standing (not part of any circuit). If you do not disconnect the resistor from the circuit, you may damage the multi-meter. b.) From I versus V graph: Draw a circuit of the unknown resistor and the power supply, and indicate where in this circuit you measure the current I and the voltage V. Construct the circuit you have just drawn. Include leads to the power supply, leads to the voltmeter, and leads to the current meter. In this circuit vary the output voltage of the power supply and measure voltage and current at least for 12 settings in the range 0 18 V, (measure the voltage V over R and the current I passing through R). V (V) I(mA) V (V) I(mA) V (V) I(mA) V (V) I(mA) Make a graphical representation ( V on horizontal axis, I on vertical axis ) and include the graph with the report. (Don t forget labeling the axes and give it an appropriate title). Ohm 9

10 How is the slope of a linear fit related to the resistance R? Do not forget the units. R unknown = Verify Ohmic behavior by checking if your data agree with Ohm s Law, i.e. how good is your linear fit. correlation =. c.) Resistance determined for the same unknown resistor from the color code: R unknown = ± The manufacturer s claimed tolerance is indicated by the last color band on the right. Is your measured value in the tolerance range given by the manufacturer? Ohm 10

11 Activity 2: Light emitting diode (LED) - non-ohmic behavior. [Do not allow more than 10 ma of current to flow through the LED to prevent damage.] A. Draw a circuit connecting a red LED in series with a 100 ~ 200 Ohm resistor connected to the power source. Where in this circuit do you measure voltage V over the LED and where do you measure current I passing through the LED? (For simplicity, measure the voltage directly over the LED.) B. Construct this circuit on the snap-on-circuit-board. Measure I and V LED for a range 0 5 V allowing only small increments in the current I and record in the table below. C. The value of current I when the red LED first lights up: ma D. The value of the voltage over the red LED, V LED when the LED first lights up: V Describe your observations that show I versus V behavior of the LED. Include a table of I versus V LED for the range 0 5 V for again at least 12 settings. Since current I may change rapidly, aim at steps of at most 0.5 ma for the current. Keep the current below 5.0 ma. Remember I-max = 10 ma!!! LED s are delicate and only allow low currents. In addition, show several data points (steps of about 0.2 ma) just above the voltage where the LED starts lighting up and the current is still small. What happens if you reverse the leads of the LED? (rotate the LED 180 degrees, leave everything else unchanged). Ohm 11

12 V LED (V) I (ma) V LED (V) I (ma) V LED (V) I (ma) V LED (V) I (ma) Make a graph showing I versus V LED (current vertical, voltage horizontal). Include also the data for reversed leads in the same graph by extending the voltage axis to include also negative values. (Reversed is equivalent to negative voltage.) Include the graph in the final report. How is this non-ohmic behavior different from Ohmic behavior? Comment on the several aspects of the behaviour shown in the graph. Ohm 12

13 Report -- RESISTANCE & OHM S LAW (Part II) Name: Section: Partners: Date: PART II Activity 3: Resistance combinations. Use the ohmmeter to measure the resistances of the three resistors you will use. Choose two of the resistances to be as closely the same value as possible and the other resistance to be at least twice as big. R 1 = R 2 = R 3 = A. Draw diagrams of all possible ways that you can connect these three resistances in series and/or parallel to give different equivalent resistances. For each diagram calculate the theoretical equivalent resistance (show your work) B. Set up two of the circuits and measure the actual value with an ohmmeter. C. Calculate the power dissipated by each resistor in the two circuits in B if a 12 V battery is connected across the circuit. [Not all entries are needed to be filled.] Circuit 1 R eq (theoretical) = R eq (experimental) = Power dissipated = diagram work Circuit 2 R eq (theoretical) = R eq (experimental) = Ohm 13

14 Power dissipated = diagram work Circuit 3 R eq (theoretical) = R eq (experimental) = Power dissipated = diagram work Circuit 4 R eq (theoretical) = R eq (experimental) = Power dissipated = diagram work Ohm 14

15 Circuit 5 R eq (theoretical) = R eq (experimental) = Power dissipated = diagram work Ohm 15

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