17 E7 E7.1 OHM'S LAW AND RESISTANCE NETWORKS OBJECT The objects of this experiment are to determine the voltage-current relationship for a resistor and to verify the series and parallel resistance formulae. EQUIPMENT In this experiment you will use a power supply, digital multimeters, and a number of resistors. Power Supply An electrical circuit is a simple example of a physical system. In this type of system there is an energy supply (a power supply or battery), an energy absorber or load (which in this lab is a resistor), and an energy transmission path linking the supply and absorber (in this case the wires AC and DB which provide a closed path or loop for the current which transmits energy from supply to load). + A Supply B C Load D The electrical system is analogous to a table-top recirculating waterfall with a water wheel at the botom. The supply is the pump which lifts the water to the top of the fountain, the absorber or load is the water wheel (which gains rotational kinetic energy due to the gravitational potential energy lost by the falling water), and the transmission path is the water itself. When the water reaches the bottom it is pumped back up to the top of the fountain and the process repeats.
18 E7.2 Depending on the type of power supply available to you, the power supply will deliver a maximum of 15 or 24 Volts at a maximum current of 1 Amp. To operate the power supply unit, first turn the voltage control knob completely counterclockwise (minimum). If the unit has a current control, turn it completely clockwise (maximum). Check that the meter switch is set to display VOLTS. Once the Power switch is turned ON, the meter will display the voltage between the red + terminal and the black terminal. When reading the meter in the voltage mode, refer to the upper scale (volts). By slowly turning the voltage knob clockwise, the output voltage can be increased. Multimeter You will use either a Circuitmate DM77 or a Beckman 310 Multimeter for measurement of DC voltage, DC current, and resistance. The instructions for use of the DM77 are given below. The instructions for use of the Beckman 310 multimeter are found at the end of this write-up. DM77: The top left switch is the power ON-OFF switch. The top right button marked AC/DC switches between AC and DC measurements. If the meter is in AC operation mode, the letters AC will appear in the top left corner of the display. If the meter is in DC mode, the letters AC disappear from the display. The central dial can be rotated to four positions. If set to the V position, the DM77 is a voltmeter. If set to the position, it is an ohmmeter. In either of the bottom two positions, the DM77 is an ammeter. Normally, the bottom 10 A position is used as it will measure currents up to 10 A. Only when you are certain that the maximum current to be measured will be less than 0.2 A should you use the 200 ma position. Making the proper connections is very important, since it prevents damage to the instrument, and determines what measurement you will be making. To measure voltage, first insert a black banana plug lead into the COM terminal. Next, insert a red banana plug lead into the V terminal. These two leads are then connected across the points in the circuit for which the potential difference (voltage) is to be measured. Normally the black lead is connected to the lower-voltage point. To use the DM77 as an ohmmeter to measure resistance, one lead is connected to the COM terminal and the other lead is connected to the -ma terminal.
19 E7.3 Circuit element to be measured Multimeter as voltmeter or ohmmeter A element whose current is to be measured Figure 2 When measuring resistance, the circuit must be disconnected from all voltage sources (power supply, battery, etc.). Also, if the circuit element across which the resistance is being measured is connected to other circuit elements, then the measured resistance may or may not equal the resistance of the desired circuit element, depending on how the other circuit elements are connected. To measure current, the current must flow through the ammeter, so the ammeter is connected in series with the circuit element whose current is to be measured (See Fig. 2). One of the leads to the circuit element is disconnected from the circuit element and connected to either the -ma or 10A terminal. The COM terminal is then connected to the circuit element. THEORY Ohm's Law states that the relationship between the voltage drop, V, across a resistor, the current, I, through the resistor, and its resistance, R, is given by V = I R (1) If a component has a constant resistance regardless of the applied voltage and current then it is said to obey Ohm s Law and is called an ohmic resistor.
20 E7.4 Resistances in Series One can show that if resistances R 1, R 2, and R 3 are connected in series as shown in Figure 3, the equivalent resistance, R S, is given by R S = R 1 + R 2 + R 3 = Sum of the individual resistances. (2) R 1 R 2 R 3 Figure 3 Resistances in Parallel Figure 4 When the resistances R 1, R 2, and R 3 are connected in R 1 parallel as shown in Figure 4, the equivalent resistance, R P, is given by R 2 1 1 1 1 R R R R (3) R 3 P 1 2 3 = Sum of the reciprocals of the individual resistances R S R P EXPERIMENT (Ohm s Law) 1. Connect the circuit as shown, using the resistor R 3 provided. Remember that current flows OUT of the + (red) terminal of the power supply, and that current must flow INTO the + terminal of the ammeter. The voltmeter is placed across (in parallel with) the load resistor, in order to measure the voltage drop across it. + Power Supply A R 3 V Figure 5 Checkpoint 1a ask the TA to review your circuit connections. Change the voltage from ~1 volt to ~10 volts in ~1 volt steps, and record the actual voltage and current each time. (For each step, both the voltage and current readings need to be stable.) Checkpoint 1b ask the TA to confirm that your data are reasonable. ANALYSIS (Ohm s Law) 2. As discussed in the tutorial, plot a graph of voltage versus current for resistor R 3 using the data that you measured in step 1. Is there a linear relationship? From the slope of the line find the resistance. Is the y-intercept of the graph consistent with the prediction of Ohm s Law?
21 Checkpoint 2 ask the TA to review your graph and your analysis of the graph. EXPERIMENT (Series and Parallel Resistor Rules) 3. Measure the resistance of each of the three resistors (R 1, R 2, R 3 ) directly by using the multimeter in the mode. Remember that the resistor to be measured must be disconnected from all other circuit elements (except the multimeter, of course!). 4. Choose the two terminals on the box of three resistances such that the resistances R 1, R 2, R 3 are connected in series and measure the total effective series resistance. 5. Connect the resistances R 1, R 2, R 3 in parallel by connecting points A and C and points B and D with jumper leads as shown in Figure 6. Now connect the multimeter at points A and D to measure the total effective parallel resistance. E7.5 Figure 6 Checkpoint 3 ask the TA to confirm that your measured individual and series and parallel resistance values are reasonable. ANALYSIS (Series and Parallel Resistor Rules) 6. Compare the directly measured value of R 3 from step 3 with the value calculated from the slope of the voltage versus current graph. Do the values agree within experimental uncertainty? 7. Calculate the theoretical series resistance using your measured values of R 1, R 2, and R 3. Compare this calculated value with the directly measured value from step 4. Do the values agree within experimental uncertainty? 8. Calculate the theoretical parallel resistance using your measured values of R 1, R 2, and R 3. Compare this calculated value with the directly measured value from step 5. Do the values agree within experimental uncertainty? Checkpoint 4 ask the TA to review your work for steps 6 through 8. CONCLUSION Discuss the significance of the shape, slope, and y-intercept of the graph of Voltage versus Current for R 3. Discuss whether or not the series and parallel resistor rules have been verified by the results of your experiment. SOURCES OF ERROR Consider whether there are factors that would change the values of the resistors as the experiment is being performed. What effect would these factors have on your results? Consider whether there are additional sources of resistance in the circuits other than the resistors themselves, and whether this would affect the results of the experiment. Checkpoint 5 ask the TA to join your discussion of your Conclusion and Sources of Error.
22 E7.6 BECKMAN 310 DIGITAL MULTIMETER The Beckman 310 Multimeter can be used to measure DC and AC voltage, DC and AC current, and resistance. DC Voltage: To measure DC voltage connect the positive lead to the leftmost input labelled V and the other lead to the COM input. The DCV section of the central dial has five divisions (200m, 2, 20, 200 and 1500) marked with the MAXIMUM voltage that can be handled without overloading the meter circuitry. The smaller numbered divisions have greater accuracy. To avoid overloading the circuitry, first turn the dial to the 1500 scale. If the voltage (or the maximum voltage expected) is less than the next lower division s maximum (200 volts) you can safely rotate the dial counter-clockwise to the next division. You can repeat this procedure until you reach the division with greatest accuracy that does NOT overload the meter. If you reach the 200m scale the meter will read in millivolts. AC Voltage: To measure AC voltage connect the leads to the V and COM inputs. Turn the dial clockwise into the ACV range. Follow a similar procedure to that described under DC Voltage to avoid overloading the meter. DC Current: To measure DC current connect the positive circuit lead to the 10A input and the other lead into the COM input. Turn the dial to the 20m/10A position in the DCA range. The meter will now read in amps to a maximum of 10 amps. If the meter reads less than 2 amps and you are sure that the maximum expected current will ALWAYS be under 2 amps, then you can safely obtain a more accurate reading by turning the meter off and reconnecting the positive lead to the A input. (NOTE: you will blow a fuse if the current ever exceeds 2 amps.) The dial can now be turned to the 2 division in the DCA range. If the current is less than 0.2 amps, turn the dial to the 200m division for greater accuracy. The meter will now read in milliamps. You can continue to switch to finer divisions providing you do NOT exceed the MAXIMUM current indicated on the dial. The finest division reads in microamps to a maximum of 200 microamps. AC Current: Follow the same procedure as described under DC Current except that the dial is rotated into the ACA range. Resistance: To measure the resistance of a circuit element, first disconnect the electrical connections of that element from any other part of the circuit. Then connect a lead from one end of the element into the ohm ( ) input and a lead from the other end into the COM input. Rotate the dial into the ohm ( ) range starting with the coarse scale (20M) where resistance will be read in Mega-ohms (M ). You can rotate the dial to finer divisions providing the resistance does NOT exceed the MAXIMUM RESISTANCE indicated. If you use the 200K, 20K or 2K divisions the resistance will read in kilo-ohms (k ). If you use the 200 division, the resistance will read in ohms ( ) to a maximum of only 200 ohms.
23 E7.7
24 E7.8 Resistors are marked with coloured bands which are interpreted according to a colour code: 0 = Black 5 = Green 1 = Brown 6 = Blue 2 = Red 7 = Violet 3 = Orange 8 = Grey 4 = Yellow 9 = White Gold: 5% Silver: 10% The first two bands give the two significant figures of the resistor value in terms of the code, the third band gives the power of 10 that multiplies the first two figures. The fourth band gives the tolerance (accuracy). If there is no fourth band, the tolerance is 20%. e.g. Yellow-Violet-Red-Silver = 47 10 2 10%
25 E7 OHM'S LAW AND RESISTANCE NETWORKS DATA & RESULTS VOLTAGE AND CURRENT DATA FOR RESISTOR R 3 Voltage, V Current, I Voltage, V Current, I ( V) ( A) ( V) ( A) RESISTANCE VALUES FOR EXPERIMENT E7 Graphical ( ) Measured ( ) Calculated ( ) R 1 R 2 R 3 R SERIES R PARALLEL
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27 Voltage versus Current for Resistor R 3 to determine relationship and resistance 10.0 9.0 8.0 7.0 Voltage, V (V) 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 Current, I (A)