where R = resistance (Ω), ρ = resistivity (Ω m), l = length (m), A = cross-sectional area (m 2 )

Transcription

1 EXPERIMENT 0 RESISTIVITY OF DIFFERENT MATERIALS NOTE: Resistivity itself is not on the study design, but is helpful to understand the nature of conduction and resistance. Your teacher will determine whether you complete this experiment. Resistivity is a property of a material that determines how well it will conduct electricity. It is independent of material dimensions, so will not change with length or thickness. The aim of this experiment is to determine the resistivity of two common metal alloys: nichrome (nickel, chromium and iron) and constantan (copper and nickel). Relevant equation where R = resistance (Ω), ρ = resistivity (Ω m), l = length (m), A = cross-sectional area (m 2 ) Equipment (pictured below) 5 metre nichrome wire board, 5 metre constantan wire board, ohm-meter (multimeter set to measure resistance). 1

2 Method 1. Using the multimeter on its resistance setting, measure the resistance of nichrome wire in 0.5 m increments up to a maximum of 5.0 m. Record your results in the table below. Length, l (m) R nichrome (Ω) R constantan (Ω) Now repeat the process using constantan wire, recording your results in the appropriate column of the table above. 3. Using Excel, for each alloy, plot a labelled graph of resistance (dependent variable) vs length (independent variable). Draw a straight line of best fit for each alloy. Remember to attach your graphs when you submit your report. 4. Calculate the cross sectional area for the wires (the diameter as stated on their original packaging is 0.46 mm). 5. By determining the gradient (R/l) of each line of best fit and using the calculated cross-sectional area (A), calculate the resistivities (ρ) of the two alloys. Ensure you express your answer in scientific notation. Remember that, unlike resistance, this is a property of the material itself, irrespective of dimensions. 6. Using the Internet, compare your calculated resistivities with the official values, offering possible reasons for any discrepency. 2

3 EXPERIMENT 1 LIGHT GLOBE FILAMENT RESISTANCE In this experiment you will vary the voltage across a mini light globe to obtain measurements of current and voltage across the globe. You will then plot the current versus voltage graph and analyse its nonohmic nature. Equipment Battery in holder, variable resistor, voltmeter, ammeter, wires, mini globe, breadboard. Method 1. Set up the following circuit. (It may help you to connect the variable resistor first and the voltmeter last.) A Globe V 2. Take the following measurements of I (current) for the set values of V (voltage) given. (If you cannot get the exact voltages below, then get as close as you can but replace the voltage in the table with your voltage.) V: Voltage (V) I: Current (ma)

4 Analysis Questions 1. Draw a scatter graph of I versus V for your set of data in Excel. Select the best fit curve and find the equation of the curve (this is done within excels options). Print a copy of the graph (or paste a copy into a word document) - it should be no smaller than ½ A4 size Graph the Voltage on the X - axis as it is the independent variable. That is, the voltage and the properties of the component determine the size of the current. 2. The resistance of the globe is given by the voltage across it divided by the current through it. Calculate the resistance of the globe at voltages of 0.05, 0.5 and 5 volts. R0.05V =... R0.5V =... R5V = Describe how the resistance of the globe changes as the voltage is increased. 4. Give an explanation for your answers to Question 2 & Is a light globe an ohmic or non-ohmic device? Explain. 6. The globe resistance values can be used to calculate the temperature of the filament using the following relationship: R T = R 0 (1 + α T) where R T is the resistance at which it is operating (5V) R 0 is the resistance at very low voltage (V 0V) α is the temperature coefficient of resistance (which is 4.4 x 10-3 K -1 for Tungsten) T is the change in temperature a) From your I-V curve for the globe, estimate R 0 and R T (for the maximum voltage that you got a reading for), and hence calculate the temperature of the filament. R 0 =... R T =... b) Any idea why does it not ignite at such a temperature? 4

5 EXPERIMENT 2 IV CURVES FOR DIODE AND RED LED DIODE (1N4004) SILVER BAND RED LED + (ANODE) + (ANODE) (CATHODE) (CATHODE) FLAT EDGE + + 5V 1. Setup the above circuit on a breadboard (see appendix A for details on breadboard). Note for the 1k potentiometer the red wire connects to +5V, black to 0V and white to ammeter. 2. Rotate the potentiometer shaft fully counter-clockwise. Power up your circuit, measure and record the voltage across and the current through the diode in the table below. 3. Rotate the potentiometer shaft (clockwise) about 10. Measure and record the voltage across and the current through the diode in the table below. 4. Repeat the above step. Take at least 20 sets of voltage and current reading for full rotation of the shaft. 5

6 5. Disconnect power from the circuit. 6. Replace the diode with a red LED, observing the correct polarity. 7. Repeat steps 2 to 4 for the red LED. 8. Plot graphs in excel (voltage on horizontal axis). DIODE (1N4004) RED LED Voltage Current Voltage Current 6

7 EXPERIMENT 3 CURRENT, POTENTIAL DIFFERENCE AND POTENTIAL AT A POINT IN DC CIRCUITS PART 1 Use the knowledge gained from series-parallel laws of resistance, Ohm s law, current and voltage laws and voltage divider theory to calculate the: 1. voltage across each resistor in the seven circuit diagrams given below. (Assume V DIODE = 0.7V and V LED = 2.0V where needed) 2. current flowing through each resistor in each circuit. This can be done by measuring the voltage drop across each resistor and the resistance of the resistor: I (current through R) = V (across R) R (measured value of resistor) X Y X Y G G X Y X Y G G 7

8 PART 2 1. Setup all four circuits, one by one on a breadboard 2. Measure the voltage across each resistor, LED and diode in each circuit. 3. Measure the current flowing through each resistor in each circuit. PART 3 1. For each of the circuits, now assume that the points labelled G are electrically grounded (i.e. 0V reference potential). An example for circuit 1 is shown below: X Y G 2. Using your calculated results from part 1, state the potentials at the points labelled X and Y for each circuit. REPORT You must explain and discuss these points: Verify your calculations with the measurements you took? What are the sources of error in this experiment? Was the battery delivering 5V? What is the accuracy of the multimeter for the different current and voltage measurements? 8

9 EXPERIMENT 4 INTERNAL RESISTANCE OF BATTERY 1. Setup the above circuit on a breadboard. For switch just use a breadboard jumper wire. Leave the switch open. 2. Select 1k resistor for R. 3. Record the voltmeter reading as battery voltage E (unloaded battery voltage) in the table below. 4. Close the switch. Record the new voltmeter reading as V, the loaded battery voltage. Also record the ammeter reading I. Caution: Take the voltmeter and ammeter reading quickly and then open the switch. 5. Repeat steps 2 to 4 for other resistors mentioned in the table below. 6. Disconnect the battery from the circuit immediatley at the end of the experiment. 7. Plot graph of E V vs I (x-axis). Find out the gradient of your graph to determine the internal resistance ( r ) of the battery. R ( ) I (ma) E (V) V (V) E V 1k

10 APPENDIX A THE ELECTRONIC BREADBOARD The modern electronics breadboard contains hundred of holes into which connecting wires, simple components and integrated circuits can be inserted. While there are variations in breadboards produced commercially they all have the same basic features: There is a central channel with no internal connection across. On each side of the channel the holes are connected internally across the width of the board. The holes are not connected internally along the length of the board. Most bread boards have 2 separate rows of internally connected holes, one at the top and the other at the bottom, which may be used to extend battery connection along the length of the board. When used in this way they are called POWER RAILS. REFER TO THE DIAGRAMS BELOW 10

11 Connecting resistors in series and parallel into a breadboard APPENDIX B ELECTRONIC RESISTORS AND THEIR COLOUR CODE Colour Number Multiplier Tolerance black brown % red % orange yellow green blue violet 7 grey 8 white 9 gold % silver % Tolerance: If the value of a resistor works out to be % from its colour code. Then the 2% tolerance value given by the manufacturer indicates that the actual value of this resistor can be anywhere in between 980 to 1020 inclusive. 11

12 Common resistor shorthand: 4.7 = 4R7 220 = 220R 1000 = 1kilo-ohm = 1k = 1k = 4.7kilo-ohm = 4.7k = 4k = 1mega-ohm = 1M = 1M = 5.6mega-ohm = 5.6M = 5M6 QUESTIONS 1. Using the colour code work out the values including its tolerance for the resistors shown below. (a) (b) % % (c) (d) % % 2. Find the colour code for the resistors given in the table below? RESISTORS FOUR BANDS FIVE BANDS k 1 39R 1 6M8 2 2k k 1 3R k 5 12

13 VOLTAGE DIVIDER THEORY APPENDIX C Voltage drop across any resistor in a series circuit can be calculated without calculating and using the series current. The supply voltage (V s ) is divided between the series resistors in a ratio. R 1 For example to calculate the voltage drop across the resistor R 2, we can use the ratio (voltage divider) formula below: V s R 2 V R2 V R 2 R 1 R R 2 2 R 3 x V S R 3 Solutions to Questions in APPENDIX B 1. (a) 82 5% (b) 1.5M 1% (c) 68k 1% (d) 10 1% 2. RESISTORS FOUR BANDS FIVE BANDS yellow, violet, brown, gold yellow, violet, black, black, gold 27k 1 red, violet, orange, brown red, violet, black, red, brown 39R 1 orange, white, black, brown orange, white, black, gold, brown 6M8 2 blue, grey, green, red blue, grey, black, yellow, red 2k2 1 red, red, red, brown red, red, black, brown, brown 560k 1 green, blue, yellow, brown green, blue, black, orange, brown 3R3 2 orange, orange, gold, red orange, orange, black, silver, red 100k 5 brown, black, yellow, gold brown, black, black, orange, gold 13