OHM'S LAW AND RESISTANCE NETWORKS OBJECT

Transcription

1 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, a digital multimeter, an ammeter, 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 (the power supply or battery), an energy absorber or load (which in this lab is a simple 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 This system is analogous to the hydraulic brake system on an automobile. The supply is the energy obtained from your foot pressure on the brake, the absorber or load is the set of brake disks and/or drums, and the transmission path is the fluid that transmits the pressure from the brake pedal to the brake disks/drums. 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.

2 18 E7.2 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 in the appendix. 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 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.

3 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) Kirchhoff's Voltage (Loop) Rule In any closed conducting loop the algebraic sum of the potential differences must be zero. i.e. The net change in potential in going around a closed loop is zero.

4 20 E7.4 Kirchhoff's Current (Junction) Rule At any junction, the net current entering must be zero. i.e. The total current entering a junction equals the total current leaving the junction. 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 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 R R R R (3) R 3 P = Sum of the reciprocals of the individual resistances PROCEDURE R S R P 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 + (red) terminal of the ammeter. The multimeter 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 Change the voltage from 1.0 volt to 10.0 volts in 1.0 volt steps, and record the current each time. Plot a graph of voltage versus current for resistor R 3. Is there a linear relationship? From the slope of the line find the resistance. Determine the y-intercept of the graph. 2. Measure the resistance of the load resistor R 3 directly by using the multimeter in the mode. Record this value of R 3. Remember that the resistor to be measured must be disconnected from all other circuit elements (except the multimeter, of course!). Compare

5 21 E7.5 this measured value with the value calculated from the slope of the voltage-current characteristic. 3. Measure and record the resistance of each of the three resistors (R 1, R 2, R 3 ) in the boxes provided. Use the multimeter in the mode for these measurements. 4. Choose the two terminals on the box of three unknown resistances such that the resistances R 1, R 2, R 3 are connected in series and measure the total effective resistance. Calculate the theoretical series resistance using your measured values of R 1, R 2, and R 3. Compare the two values. 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 resistance. Calculate the theoretical parallel resistance using your measured values of R 1, R 2, and R 3. Compare the two values. Figure 6 CONCLUSION Discuss the significance of the shape 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. 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.

6 22 E7.6 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 = %

7 23 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

8 Voltage versus Current for Resistor R 3 to determine relationship and resistance Voltage, V (V) Current, I (A)